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School: Caltech
Course: CS 21
CS 21 Decidability and Tractability Winter 2012 Final Exam Solutions Posted: March 16 If you have not turned in the nal, obviously you should not consult these solutions. 1. (a) First, the problem is in PSPACE, for the usual reason for 2-player games. Giv
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Midterm Out: February 6 Due: February 13 This is a midterm. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: CS 21
CS 21 Decidability and Tractability Winter 2012 Problem Set 1 Out: January 11 Due: January 18 Reminder: you are encouraged to work in groups of two or three; however you must turn in your own write-up and note with whom you worked. You may consult the cou
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2012 Midterm Solutions Out: February 13 1. (a) The language L1 is context free but not regular. To see it is context free, consider the NPDA that rst pushes as onto the stack until it sees the rst b, then pops as
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Final Out: March 13 Due: March 20, noon This is a nal exam. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: Python
Linus Torvalds CS 1 Linux Tutorial September 29, 2010 Linux mascot Linux: Introduction You've probably heard of the Windows and Mac OS X operating systems Linux is another popular one (its free too!) All the CS cluster machines run Linux CS cluster = co
School: Caltech
Course: Logic Model Checking For Formal Software Verification
1 2 3 4 5 6 7 8 9 10 11 12 13
School: Caltech
Course: Quantum Computation
CS 294-2 Spring 2007 Abelian HSP + Discrete Log Lecture 9 2/14/07 Abelian Hidden Subgroup Problem + Discrete Log 1 Fourier transforms over nite abelian groups Let G be a nite abelian group. The characters of G are homomorphisms j : G C. There are exactly
School: Caltech
CS/Ec133 Notes - DRAFT John O. Ledyard October 13, 2013 BEWARE. These are notes intended to capture (and augment and correct) presentations from classes on these subjects. They are hastily written (I do not want to be a book author) and so are not serious
School: Caltech
Course: Complexity Theory
Complexity Theory Classify problems according to the computational resources required CS151 Complexity Theory Lecture 1 April 2, 2013 running time storage space parallelism randomness rounds of interaction, communication, others Attempt to answer: what is
School: Caltech
Course: Complexity Theory
Extended Church-Turing Thesis consequence of extended Church-Turing Thesis: all reasonable physically realizable models of computation can be efficiently simulated by a TM CS151 Complexity Theory Lecture 2 April 4, 2013 e.g. multi-tape vs. single tape T
School: Caltech
Course: Complexity Theory
Robust Time and Space Classes Robust time and space classes: CS151 Complexity Theory L = SPACE(log n) PSPACE = k SPACE(nk) Lecture 3 April 9, 2013 P = k TIME(nk) k EXP = k TIME(2n ) April 9, 2013 Relationships between classes A P-complete problem So far
School: Caltech
CS21 Decidability and Tractability Lecture 9 January 27, 2014 January 27, 2014 CS21 Lecture 8 1 Outline Turing Machines and variants multitape TMs nondeterministic TMs Church-Turing Thesis decidable, RE, co-RE languages January 27, 2014 CS21 Lecture 8 2 T
School: Caltech
CS21 Decidability and Tractability Lecture 7 January 22, 2014 January 22, 2014 CS21 Lecture 7 1 Outline proof of CFL pumping lemma deterministic PDAs deciding CFLs January 22, 2014 CS21 Lecture 7 2 Pumping Lemma for CFLs CFL Pumping Lemma: Let L be a CFL.
School: Caltech
CS21 Decidability and Tractability Lecture 8 January 24, 2014 January 24, 2014 CS21 Lecture 8 1 Outline deterministic PDAs deciding CFLs Turing Machines and variants January 24, 2014 CS21 Lecture 8 2 Deterministic PDA A technical detail: we will give our
School: Caltech
CS21 Decidability and Tractability Lecture 4 January 13, 2014 January 13, 2014 CS21 Lecture 3 1 Outline Pumping Lemma Pushdown Automata Context-Free Grammars and Languages January 13, 2014 CS21 Lecture 3 2 Non-regular languages Pumping Lemma: Let L be a r
School: Caltech
CS21 Decidability and Tractability Lecture 2 January 8, 2014 January 8, 2014 CS21 Lecture 2 1 Outline Finite Automata Nondeterministic Finite Automata Closure under regular operations NFA, FA equivalence January 8, 2014 CS21 Lecture 2 2 Terminology finit
School: Caltech
CS21 Decidability and Tractability Lecture 6 January 17, 2014 January 17, 2014 CS21 Lecture 6 1 Outline equivalence of NPDAs and CFGs non context-free languages deterministic PDAs January 17, 2014 CS21 Lecture 6 2 Context-Free Grammars start symbol A 0A1
School: Caltech
Course: CS 21
CS 21 Decidability and Tractability Winter 2012 Final Exam Solutions Posted: March 16 If you have not turned in the nal, obviously you should not consult these solutions. 1. (a) First, the problem is in PSPACE, for the usual reason for 2-player games. Giv
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Midterm Out: February 6 Due: February 13 This is a midterm. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Final Out: March 13 Due: March 20, noon This is a nal exam. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: Computation, Computers, And Programs
Quiz3 1. (10) Prove that equality i = j of partial recursive functions is undecidable. 2. (10) Show that the time-bounded while-programs are primitive recursive. The time-bounded programs are defined as follows. For any while loop while x y do e done, the
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Final Solutions Posted: June 10 Chris Umans 1. (a) The procedure that traverses a fan-in 2 depth O(logi n) circuit and outputs a formula runs in Li this can be done by a recursive depth-rst traversal, which only requir
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Midterm Solutions Posted: May 9 Chris Umans 1. Consider a language L coNEXP. On an input of length n, the advice will be an exact count of the number of inputs of length n not in the language. This is a number between
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 First Assignment This assignment counts for 10% of the final grade. (late submissions lose 10 pts from the score, cumulatively each day at noon) Solutions are due: Noon, 22 January 2013 via email to gerard@spinroot.com (plain
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Second Assignment This assignment counts for 10% of the final grade. (late submissions lose 10 pts from the score, cumulatively each day at noon) Solutions are due: Noon, 29 January 2013 via email to gerard@spinroot.com (plain
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Third Assignment This assignment counts for 10% of the final grade. Solutions are due: Noon, 5 February 2013 (10 pts are deducted if submitted late, cumulatively each day at noon) via email to gerard@spinroot.com 1) (20 pts) C
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Fourth Assignment This assignment counts for 10% of the final grade. Solutions are due: Noon, Thursday 14 February 2013 Reminder: there is no lecture on Tuesday February 12. (10 pts deducted if submitted late, cumulatively eac
School: Caltech
October 14, 2013 Ec/CS 133 Problem Set #1 revised Answers due Monday October 21 , 5 PM in box outside of my oce Baxter 102. Question 1 A company has 2 plants with which it can produce units of output. The cost functions 2 2 of the plants are C 1 (y1 ) = 1
School: Caltech
November 3, 2013 Ec/CS 133 Problem Set #2 Problems due Nov 13, in class. Question 1 There is a 3 bus power system. On node 1 there is a generator B and a 400 MW load. On node 2 there is a generator A and an 80 MW load. On node 3 there are 2 generators, C
School: Caltech
Course: Computer Language Shop
C track: assignment 5 Goals In this assignment you will write a program to simulate a simple one-dimensional cellular automaton, which are related to (but are not the same as) two-dimensional cellular automata like Conway's game of Life. We will use this
School: Caltech
Course: Computer Language Shop
C track: assignment 8: Implementing a virtual machine Goals This lab is the last assignment in this track. By now you know almost all the important aspects of the C language, with the exception of a few features like function pointers which aren't really
School: Caltech
Course: Computer Language Shop
C track: assignment 7 Goals This week, we are going to move beyond a discussion of built-in features of the C language (we've covered most of them already) and continue discussing how to implement fundamental data structures in C. The data structure we wi
School: Caltech
Course: Computer Language Shop
C track: assignment 6 Goals In this assignment you will write a sorting program similar to the program from lab 3, except that it uses linked lists instead of arrays to hold the list of numbers read in off the command line. In the process, you will learn
School: Caltech
Fall 2013 Syllabus CS/EC 133: Electricity Markets Meets Wednesday- Friday: 1- 230 pm in Baxter 25. Instructor: John Ledyard Office: Baxter 102, x8482, Email: jledyard@caltech.edu, Office Hours:
School: Caltech
Course: Decidability And Tractability
CS21: Decidability and Tractability course information and tentative schedule Catalog description: This course introduces the formal foundations of computer science, the fundamental limits of computation, and the limits of ecient computation. Topics will
School: Caltech
CS 151 Complexity Theory Spring 2011 Course Summary and Syllabus Lecturer: Chris Umans Date: March 29 Course summary: Complexity Theory attempts to answer the question: What is computationally feasible given limited computational resources? In this course
School: Caltech
CS 9 Introduction to Computer Science Research Fall 2011 Course Summary and Syllabus Date: October 5 This course will introduce the research areas of the computer science faculty, through weekly overview talks by the faculty aimed at rst-year undergraduat
School: Caltech
Course: CS 21
CS 21 Decidability and Tractability Winter 2012 Final Exam Solutions Posted: March 16 If you have not turned in the nal, obviously you should not consult these solutions. 1. (a) First, the problem is in PSPACE, for the usual reason for 2-player games. Giv
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Midterm Out: February 6 Due: February 13 This is a midterm. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: CS 21
CS 21 Decidability and Tractability Winter 2012 Problem Set 1 Out: January 11 Due: January 18 Reminder: you are encouraged to work in groups of two or three; however you must turn in your own write-up and note with whom you worked. You may consult the cou
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2012 Midterm Solutions Out: February 13 1. (a) The language L1 is context free but not regular. To see it is context free, consider the NPDA that rst pushes as onto the stack until it sees the rst b, then pops as
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Final Out: March 13 Due: March 20, noon This is a nal exam. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: Python
Linus Torvalds CS 1 Linux Tutorial September 29, 2010 Linux mascot Linux: Introduction You've probably heard of the Windows and Mac OS X operating systems Linux is another popular one (its free too!) All the CS cluster machines run Linux CS cluster = co
School: Caltech
Course: Logic Model Checking For Formal Software Verification
1 2 3 4 5 6 7 8 9 10 11 12 13
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 First Assignment This assignment counts for 10% of the final grade. (late submissions lose 10 pts from the score, cumulatively each day at noon) Solutions are due: Noon, 22 January 2013 via email to gerard@spinroot.com (plain
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Second Assignment This assignment counts for 10% of the final grade. (late submissions lose 10 pts from the score, cumulatively each day at noon) Solutions are due: Noon, 29 January 2013 via email to gerard@spinroot.com (plain
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Third Assignment This assignment counts for 10% of the final grade. Solutions are due: Noon, 5 February 2013 (10 pts are deducted if submitted late, cumulatively each day at noon) via email to gerard@spinroot.com 1) (20 pts) C
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Fourth Assignment This assignment counts for 10% of the final grade. Solutions are due: Noon, Thursday 14 February 2013 Reminder: there is no lecture on Tuesday February 12. (10 pts deducted if submitted late, cumulatively eac
School: Caltech
Course: Quantum Computation
CS 294-2 Spring 2007 Abelian HSP + Discrete Log Lecture 9 2/14/07 Abelian Hidden Subgroup Problem + Discrete Log 1 Fourier transforms over nite abelian groups Let G be a nite abelian group. The characters of G are homomorphisms j : G C. There are exactly
School: Caltech
CS21 Decidability and Tractability Lecture 9 January 27, 2014 January 27, 2014 CS21 Lecture 8 1 Outline Turing Machines and variants multitape TMs nondeterministic TMs Church-Turing Thesis decidable, RE, co-RE languages January 27, 2014 CS21 Lecture 8 2 T
School: Caltech
CS21 Decidability and Tractability Lecture 7 January 22, 2014 January 22, 2014 CS21 Lecture 7 1 Outline proof of CFL pumping lemma deterministic PDAs deciding CFLs January 22, 2014 CS21 Lecture 7 2 Pumping Lemma for CFLs CFL Pumping Lemma: Let L be a CFL.
School: Caltech
CS21 Decidability and Tractability Lecture 8 January 24, 2014 January 24, 2014 CS21 Lecture 8 1 Outline deterministic PDAs deciding CFLs Turing Machines and variants January 24, 2014 CS21 Lecture 8 2 Deterministic PDA A technical detail: we will give our
School: Caltech
CS21 Decidability and Tractability Lecture 4 January 13, 2014 January 13, 2014 CS21 Lecture 3 1 Outline Pumping Lemma Pushdown Automata Context-Free Grammars and Languages January 13, 2014 CS21 Lecture 3 2 Non-regular languages Pumping Lemma: Let L be a r
School: Caltech
CS21 Decidability and Tractability Lecture 2 January 8, 2014 January 8, 2014 CS21 Lecture 2 1 Outline Finite Automata Nondeterministic Finite Automata Closure under regular operations NFA, FA equivalence January 8, 2014 CS21 Lecture 2 2 Terminology finit
School: Caltech
CS21 Decidability and Tractability Lecture 6 January 17, 2014 January 17, 2014 CS21 Lecture 6 1 Outline equivalence of NPDAs and CFGs non context-free languages deterministic PDAs January 17, 2014 CS21 Lecture 6 2 Context-Free Grammars start symbol A 0A1
School: Caltech
CS21 Decidability and Tractability Lecture 5 January 15, 2014 January 15, 2014 CS21 Lecture 5 1 Outline Pushdown Automata Context-Free Grammars and Languages parse trees ambiguity normal form equivalence of NPDAs and CFGs January 15, 2014 CS21 Lecture
School: Caltech
CS21 Decidability and Tractability Lecture 3 January 10, 2014 January 10, 2014 CS21 Lecture 3 1 Outline Regular Expressions FA and Regular Expressions Pumping Lemma January 10, 2014 CS21 Lecture 3 2 Next Describe the set of languages that can be built up
School: Caltech
CS21 Decidability and Tractability Lecture 1 January 6, 2014 January 6, 2014 CS21 Lecture 1 1 Outline administrative stuff motivation and overview of the course problems and languages Finite Automata January 6, 2014 CS21 Lecture 1 2 Administrative Stuff
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 8 Last week: hash tables, C preprocessor This week: Other integral types: short, long, unsigned bitwise operators switch "fun" assignment: virtual machine Integral types (1) Usually use int to represent integers But many other integ
School: Caltech
Course: Computer Language Shop
C track: assignment 5 Goals In this assignment you will write a program to simulate a simple one-dimensional cellular automaton, which are related to (but are not the same as) two-dimensional cellular automata like Conway's game of Life. We will use this
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 7 Last week: structs, typedef, linked lists This week: hash tables more on the C preprocessor extern const Hash tables (1) Data structures we've seen so far: arrays structs linked lists Hash tables (2) Hash tables are a new data
School: Caltech
Course: Computer Language Shop
C track: assignment 8: Implementing a virtual machine Goals This lab is the last assignment in this track. By now you know almost all the important aspects of the C language, with the exception of a few features like function pointers which aren't really
School: Caltech
Course: Computer Language Shop
C track: assignment 7 Goals This week, we are going to move beyond a discussion of built-in features of the C language (we've covered most of them already) and continue discussing how to implement fundamental data structures in C. The data structure we wi
School: Caltech
Course: Computer Language Shop
C track: assignment 6 Goals In this assignment you will write a sorting program similar to the program from lab 3, except that it uses linked lists instead of arrays to hold the list of numbers read in off the command line. In the process, you will learn
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 3 This week: Arrays one-dimensional multidimensional Command-line arguments Assertions Arrays What is an "array"? A way to collect together data of a single type in a single object A linear sequence of data objects e.g. array of int
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 6 n n Last week: pointer arithmetic This week: n The gdb program struct typedef linked lists n n n gdb for debugging (1) n n gdb: the Gnu DeBugger http:/www.cs.caltech.edu/courses/cs11/ material/c/mike/misc/gdb.html Use when program
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 4 Last week: arrays This week: Recursion Introduction to pointers Lab 4 Harder than previous labs One non-obvious trick hints on web page email me if get stuck Support code supplied for you Read carefully! Recursion (1) Should be fa
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 5 n n Last week: pointers This week: n n n n Pointer arithmetic Arrays and pointers Dynamic memory allocation The stack and the heap Pointers (from last week) n n Address: location where data stored Pointer: variable that holds an a
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 1 Preliminaries Need a CS (CMS) cluster account Need to know UNIX http:/acctreq.cms.caltech.edu/cgi-bin/request.cgi ITS tutorial linked from track home page Track home page: http:/courses.cms.caltech.edu/cs11/material/c/ mike/index.
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 2 Last week: basics of C programming compilation data types (int, float, double, char, etc.) operators (+ - * / = = += etc.) functions conditionals loops preprocessor (#include) This week Preprocessor (#define) Operators and precede
School: Caltech
1 + + + + + + + + + + x2 1 x1 1 x 1 l L (l) xj = d s l = L (s) xd + + h (x ) (l1) (l) j (l ) wij = xi (l1) (l) wij i=0 (s) = tanh(s) (l1) xi d( l ) (l1) i (l) (l1) 2 = (1 (xi ) (l) wij j j =1
School: Caltech
g h 1 , h2 , , hM Hi |E (g ) E (g )| > Eout(h) |E (h1) E (h1)| > |E (h2) E (h2)| > |E (hM ) E (hM )| > Ein(h) Hi P[ 22N |E (h) E (h)| > ] 2e M
School: Caltech
x0 x1 s h(x) x2 xd E (s) w w(0) (ynwxn) P (yn | xn) = n=1 w(t + 1) = w(t) E (w(t) N N n=1 t = 0, 1, 2, w N 1 E (w) = N h(xn), yn n=1 ln(1+eynw xn )
School: Caltech
d wixi = w x i=0 h(x) = (wx) h(x) = wx 1 w = (X X) X y y x1 x2 wx w x z (x1, x2) (x2, x2) 12
School: Caltech
mH(N ) H N 1 2 3 4 5 6 : 1 1 1 1 1 1 1 : Hoeffding Inequality Union Bound VC Bound k k 23456 22222 34444 4 7 top 8 8 8 5 11 . . . . . . 6: . 7: . : . bottom k1 mH(N ) i=0 . . . . . . . . . . N i N k1 space of data sets . D (a) [ |E (b) (c) [ |E
School: Caltech
d(H) 10 10 5 10 H 0 10 5 10 up 20 UNKNOWN TARGET FUNCTION f: X Y 80 100 120 140 160 180 200 N d DISTRIBUTION on X TRAINING EXAMPLES ( x1 , y1 ), . , ( xN , y ) N ALGORITHM 60 PROBABILITY P LEARNING 40 FINAL HYPOTHESIS g~f ~ A E HYPOTH
School: Caltech
y = f (x) h(x), f (x) 8 >+1 < > : 1 1 E (h) = N target function f: x) XY plus noise TRAINING EXAMPLES ( x1 , y1 ), . , ( xN , y ) N UNKNOWN INPUT DISTRIBUTION P (x) N h(xn), f (xn) n=1 (x1, y1), , (xN , yN ) E (h) = Ex P (x, y ) = P (x)P (y
School: Caltech
mH(N )= max x1, ,xN X |H(x1, , xN )| x1 x2 x3 mH(N ) mH(N ) M mH(N ) mH(N ) mH(N ) B (N, k ) N
School: Caltech
Fall 2013 Syllabus CS/EC 133: Electricity Markets Meets Wednesday- Friday: 1- 230 pm in Baxter 25. Instructor: John Ledyard Office: Baxter 102, x8482, Email: jledyard@caltech.edu, Office Hours:
School: Caltech
A generator exercises market power if they move the market price above the competitive equilibrium price and make a prot doing so. We have seen (in the CA crisis) how the owner of multiple generators might do so by withholding a unit. Why is this an issue
School: Caltech
public goods: quasi-linear preferences J Ledyard November 26, 2013 We consider an extreme form of market failure - Public Goods A public good is - non-rivalrous (whatever you consume does not subtract from what I can consumer) and - non-excludeable (no on
School: Caltech
What is the problem? See Example 2A in section 3-9 of text. Two issues: market decentralization and computation 1 The general least cost dispatch problem: min K k=1 T t=1 cktxkt + zkt(1 zkt)sk t subject to (xk , zk ) Sk , zk cfw_0, 1T , k xkt = Dt plus ot
School: Caltech
Lecture 5 Firms - a deeper look J Ledyard October 8, 2013 USC 1 A rm takes a bundle of inputs z L and produces y . The production function captures the technological possibilities of the rm. y = f (z ). The cost function of the rm is derived from the prod
School: Caltech
GA GB LZ 1 2 Z = 0.2 Z = 0. 2 Gc Lx 3 Gd LY Loads Z = 50 X = 60 Y = 300 Generator Capacity, Mar. cost A 140 7.5 B 285 6 C 90 14 D 85 10 Lines Imp., Capacity 12
School: Caltech
CS/EC 133 lecture 2 Many commodities Many markets Multiple units Many commodities Multiple units Renters want to consider different sqft Renters want more than one room Landlords own multiple units of different sizes Multiple commodities Renting a room to
School: Caltech
CSEC 133: Lecture 3 Optimization J Ledyard October 8, 2013 1 Unconstrained Optimization f: N . We assume f C 2. If x solves max f (x), then x f (x ) = (f /x1 , .) = 0. 2 Unconstrained Optimization f: N . We assume f C 2. If x solves max f (x), then x f (x
School: Caltech
CS/EC 133 lecture 2 Simple economics review 1 Simple environment Example Tourists coming to town: each needs a room Landlords: each has identical room Questions Who gets a room? Who sells a room? How much do they pay? Is there an optimal allocation? 2 Th
School: Caltech
CS/Ec133 Notes - DRAFT John O. Ledyard October 13, 2013 BEWARE. These are notes intended to capture (and augment and correct) presentations from classes on these subjects. They are hastily written (I do not want to be a book author) and so are not serious
School: Caltech
GA GB LZ 1 2 Z = 0.2 Z = 0. 2 Gc Lx 3 Gd LY Loads Z = 50 X = 60 Y = 300 Generator Capacity, Mar. cost A 140 7.5 B 285 6 C 90 14 D 85 10 Lines Imp., Capacity 12
School: Caltech
Because of the demand side aws, no real-time metering and no real-time control, and because the least-cost dispatch problem cannot be run every second, there is almost always a mis-match between load and generation. 1 Top is typical load and generation pr
School: Caltech
eeh power systems laboratory Harnessing Residential Loads for Demand Response: Engineering and Economic Considerations Dr. Johanna L. Mathieu, Tobias Haring, and Prof. Gran Andersson Power Systems Laboratory, ETH Zrich with contributions from Prof. Duncan
School: Caltech
Reminder : Transmission & Decentralized Trading BUS A BUS B G1 L2 G2 L1 L1 = 500, MC1= 10 + .01 P1, L2 = 1500, MC2 = 13 + .02 P2 A B 500 1500 Autarky a=15, b= 43 No Constraints
School: Caltech
Power struggle: Green energy versus a grid that's not ready - lat. Like Log In 682k Member Center http:/www.latimes.com/nation/la-na-grid-renewables-20131203. Alerts & Newsletters Jobs Cars Real Estate Rentals Weekly Circulars STYLE TRAVEL OPINION Local D
School: Caltech
Reminder : Transmission & Decentralized Trading BUS A BUS B G1 L2 G2 L1 L1 = 500, MC1= 10 + .01 P1, L2 = 1500, MC2 = 13 + .02 P2 A B 500 1500 Autarky a=15, b= 43 No Constraints
School: Caltech
Course: Logic Model Checking For Formal Software Verification
1 2 3 4 5 6 7 8 9 10 11 12 13
School: Caltech
Course: Quantum Computation
CS 294-2 Spring 2007 Abelian HSP + Discrete Log Lecture 9 2/14/07 Abelian Hidden Subgroup Problem + Discrete Log 1 Fourier transforms over nite abelian groups Let G be a nite abelian group. The characters of G are homomorphisms j : G C. There are exactly
School: Caltech
CS/Ec133 Notes - DRAFT John O. Ledyard October 13, 2013 BEWARE. These are notes intended to capture (and augment and correct) presentations from classes on these subjects. They are hastily written (I do not want to be a book author) and so are not serious
School: Caltech
Course: Complexity Theory
Complexity Theory Classify problems according to the computational resources required CS151 Complexity Theory Lecture 1 April 2, 2013 running time storage space parallelism randomness rounds of interaction, communication, others Attempt to answer: what is
School: Caltech
Course: Complexity Theory
Extended Church-Turing Thesis consequence of extended Church-Turing Thesis: all reasonable physically realizable models of computation can be efficiently simulated by a TM CS151 Complexity Theory Lecture 2 April 4, 2013 e.g. multi-tape vs. single tape T
School: Caltech
Course: Complexity Theory
Robust Time and Space Classes Robust time and space classes: CS151 Complexity Theory L = SPACE(log n) PSPACE = k SPACE(nk) Lecture 3 April 9, 2013 P = k TIME(nk) k EXP = k TIME(2n ) April 9, 2013 Relationships between classes A P-complete problem So far
School: Caltech
Course: Complexity Theory
Ladners Theorem Assuming P NP, what does the world (inside NP) look like? CS151 Complexity Theory NP: NPC NPC P Lecture 4 April 11, 2013 NP: P April 11, 2013 Ladners Theorem 2 Ladners Theorem Theorem (Ladner): If P NP, then there exists L NP that is neit
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EE 150 Presentation Week 6 L. Xiao, M. Johansson, H. Hindi, S. Boyd, A. Goldsmith: "Joint Optimization of Communication Rates and Linear Systems" Ather Gattami, May 6, 2003 1 Problem Setup w LTI System z yr Network y w: exogenous signal, including noises
School: Caltech
The International Journal of Biochemistry & Cell Biology 41 (2009) 254265 Contents lists available at ScienceDirect The International Journal of Biochemistry & Cell Biology journal homepage: www.elsevier.com/locate/biocel Review Evolutionary origins and d
School: Caltech
Course: Introduction To Computer Science
CS1: Introduction to Computation Midterm Review Caltech CS 1 - Fall 2008 Midterm . on the web site Real Soon Now Find linked from CS 1 home page and in "schedule" section Due date: Tuesday, November 4, 5 PM Lab 5 also due Thurs night 2am (Nov. 6) yes,
School: Caltech
Course: Learning Complexity
Cant Decide? Undecide! Chaim Goodman-Strauss In my mathematical youth, when I rst learned of Gdels Theorem, and computational undecidability, o I was at once fascinated and strangely reassured of our limited place in the grand universe: incredibly mathema
School: Caltech
CS21 Decidability and Tractability Lecture 9 January 27, 2014 January 27, 2014 CS21 Lecture 8 1 Outline Turing Machines and variants multitape TMs nondeterministic TMs Church-Turing Thesis decidable, RE, co-RE languages January 27, 2014 CS21 Lecture 8 2 T
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CS21 Decidability and Tractability Lecture 7 January 22, 2014 January 22, 2014 CS21 Lecture 7 1 Outline proof of CFL pumping lemma deterministic PDAs deciding CFLs January 22, 2014 CS21 Lecture 7 2 Pumping Lemma for CFLs CFL Pumping Lemma: Let L be a CFL.
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CS21 Decidability and Tractability Lecture 8 January 24, 2014 January 24, 2014 CS21 Lecture 8 1 Outline deterministic PDAs deciding CFLs Turing Machines and variants January 24, 2014 CS21 Lecture 8 2 Deterministic PDA A technical detail: we will give our
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CS21 Decidability and Tractability Lecture 4 January 13, 2014 January 13, 2014 CS21 Lecture 3 1 Outline Pumping Lemma Pushdown Automata Context-Free Grammars and Languages January 13, 2014 CS21 Lecture 3 2 Non-regular languages Pumping Lemma: Let L be a r
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CS21 Decidability and Tractability Lecture 2 January 8, 2014 January 8, 2014 CS21 Lecture 2 1 Outline Finite Automata Nondeterministic Finite Automata Closure under regular operations NFA, FA equivalence January 8, 2014 CS21 Lecture 2 2 Terminology finit
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CS21 Decidability and Tractability Lecture 6 January 17, 2014 January 17, 2014 CS21 Lecture 6 1 Outline equivalence of NPDAs and CFGs non context-free languages deterministic PDAs January 17, 2014 CS21 Lecture 6 2 Context-Free Grammars start symbol A 0A1
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CS21 Decidability and Tractability Lecture 5 January 15, 2014 January 15, 2014 CS21 Lecture 5 1 Outline Pushdown Automata Context-Free Grammars and Languages parse trees ambiguity normal form equivalence of NPDAs and CFGs January 15, 2014 CS21 Lecture
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CS21 Decidability and Tractability Lecture 3 January 10, 2014 January 10, 2014 CS21 Lecture 3 1 Outline Regular Expressions FA and Regular Expressions Pumping Lemma January 10, 2014 CS21 Lecture 3 2 Next Describe the set of languages that can be built up
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CS21 Decidability and Tractability Lecture 1 January 6, 2014 January 6, 2014 CS21 Lecture 1 1 Outline administrative stuff motivation and overview of the course problems and languages Finite Automata January 6, 2014 CS21 Lecture 1 2 Administrative Stuff
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 8 Last week: hash tables, C preprocessor This week: Other integral types: short, long, unsigned bitwise operators switch "fun" assignment: virtual machine Integral types (1) Usually use int to represent integers But many other integ
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Course: Computer Language Shop
CS 11 C track: lecture 7 Last week: structs, typedef, linked lists This week: hash tables more on the C preprocessor extern const Hash tables (1) Data structures we've seen so far: arrays structs linked lists Hash tables (2) Hash tables are a new data
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 3 This week: Arrays one-dimensional multidimensional Command-line arguments Assertions Arrays What is an "array"? A way to collect together data of a single type in a single object A linear sequence of data objects e.g. array of int
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 6 n n Last week: pointer arithmetic This week: n The gdb program struct typedef linked lists n n n gdb for debugging (1) n n gdb: the Gnu DeBugger http:/www.cs.caltech.edu/courses/cs11/ material/c/mike/misc/gdb.html Use when program
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 4 Last week: arrays This week: Recursion Introduction to pointers Lab 4 Harder than previous labs One non-obvious trick hints on web page email me if get stuck Support code supplied for you Read carefully! Recursion (1) Should be fa
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 5 n n Last week: pointers This week: n n n n Pointer arithmetic Arrays and pointers Dynamic memory allocation The stack and the heap Pointers (from last week) n n Address: location where data stored Pointer: variable that holds an a
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 1 Preliminaries Need a CS (CMS) cluster account Need to know UNIX http:/acctreq.cms.caltech.edu/cgi-bin/request.cgi ITS tutorial linked from track home page Track home page: http:/courses.cms.caltech.edu/cs11/material/c/ mike/index.
School: Caltech
Course: Computer Language Shop
CS 11 C track: lecture 2 Last week: basics of C programming compilation data types (int, float, double, char, etc.) operators (+ - * / = = += etc.) functions conditionals loops preprocessor (#include) This week Preprocessor (#define) Operators and precede
School: Caltech
1 + + + + + + + + + + x2 1 x1 1 x 1 l L (l) xj = d s l = L (s) xd + + h (x ) (l1) (l) j (l ) wij = xi (l1) (l) wij i=0 (s) = tanh(s) (l1) xi d( l ) (l1) i (l) (l1) 2 = (1 (xi ) (l) wij j j =1
School: Caltech
g h 1 , h2 , , hM Hi |E (g ) E (g )| > Eout(h) |E (h1) E (h1)| > |E (h2) E (h2)| > |E (hM ) E (hM )| > Ein(h) Hi P[ 22N |E (h) E (h)| > ] 2e M
School: Caltech
x0 x1 s h(x) x2 xd E (s) w w(0) (ynwxn) P (yn | xn) = n=1 w(t + 1) = w(t) E (w(t) N N n=1 t = 0, 1, 2, w N 1 E (w) = N h(xn), yn n=1 ln(1+eynw xn )
School: Caltech
d wixi = w x i=0 h(x) = (wx) h(x) = wx 1 w = (X X) X y y x1 x2 wx w x z (x1, x2) (x2, x2) 12
School: Caltech
mH(N ) H N 1 2 3 4 5 6 : 1 1 1 1 1 1 1 : Hoeffding Inequality Union Bound VC Bound k k 23456 22222 34444 4 7 top 8 8 8 5 11 . . . . . . 6: . 7: . : . bottom k1 mH(N ) i=0 . . . . . . . . . . N i N k1 space of data sets . D (a) [ |E (b) (c) [ |E
School: Caltech
d(H) 10 10 5 10 H 0 10 5 10 up 20 UNKNOWN TARGET FUNCTION f: X Y 80 100 120 140 160 180 200 N d DISTRIBUTION on X TRAINING EXAMPLES ( x1 , y1 ), . , ( xN , y ) N ALGORITHM 60 PROBABILITY P LEARNING 40 FINAL HYPOTHESIS g~f ~ A E HYPOTH
School: Caltech
y = f (x) h(x), f (x) 8 >+1 < > : 1 1 E (h) = N target function f: x) XY plus noise TRAINING EXAMPLES ( x1 , y1 ), . , ( xN , y ) N UNKNOWN INPUT DISTRIBUTION P (x) N h(xn), f (xn) n=1 (x1, y1), , (xN , yN ) E (h) = Ex P (x, y ) = P (x)P (y
School: Caltech
mH(N )= max x1, ,xN X |H(x1, , xN )| x1 x2 x3 mH(N ) mH(N ) M mH(N ) mH(N ) mH(N ) B (N, k ) N
School: Caltech
A generator exercises market power if they move the market price above the competitive equilibrium price and make a prot doing so. We have seen (in the CA crisis) how the owner of multiple generators might do so by withholding a unit. Why is this an issue
School: Caltech
public goods: quasi-linear preferences J Ledyard November 26, 2013 We consider an extreme form of market failure - Public Goods A public good is - non-rivalrous (whatever you consume does not subtract from what I can consumer) and - non-excludeable (no on
School: Caltech
What is the problem? See Example 2A in section 3-9 of text. Two issues: market decentralization and computation 1 The general least cost dispatch problem: min K k=1 T t=1 cktxkt + zkt(1 zkt)sk t subject to (xk , zk ) Sk , zk cfw_0, 1T , k xkt = Dt plus ot
School: Caltech
Lecture 5 Firms - a deeper look J Ledyard October 8, 2013 USC 1 A rm takes a bundle of inputs z L and produces y . The production function captures the technological possibilities of the rm. y = f (z ). The cost function of the rm is derived from the prod
School: Caltech
GA GB LZ 1 2 Z = 0.2 Z = 0. 2 Gc Lx 3 Gd LY Loads Z = 50 X = 60 Y = 300 Generator Capacity, Mar. cost A 140 7.5 B 285 6 C 90 14 D 85 10 Lines Imp., Capacity 12
School: Caltech
CS/EC 133 lecture 2 Many commodities Many markets Multiple units Many commodities Multiple units Renters want to consider different sqft Renters want more than one room Landlords own multiple units of different sizes Multiple commodities Renting a room to
School: Caltech
CSEC 133: Lecture 3 Optimization J Ledyard October 8, 2013 1 Unconstrained Optimization f: N . We assume f C 2. If x solves max f (x), then x f (x ) = (f /x1 , .) = 0. 2 Unconstrained Optimization f: N . We assume f C 2. If x solves max f (x), then x f (x
School: Caltech
CS/EC 133 lecture 2 Simple economics review 1 Simple environment Example Tourists coming to town: each needs a room Landlords: each has identical room Questions Who gets a room? Who sells a room? How much do they pay? Is there an optimal allocation? 2 Th
School: Caltech
GA GB LZ 1 2 Z = 0.2 Z = 0. 2 Gc Lx 3 Gd LY Loads Z = 50 X = 60 Y = 300 Generator Capacity, Mar. cost A 140 7.5 B 285 6 C 90 14 D 85 10 Lines Imp., Capacity 12
School: Caltech
Because of the demand side aws, no real-time metering and no real-time control, and because the least-cost dispatch problem cannot be run every second, there is almost always a mis-match between load and generation. 1 Top is typical load and generation pr
School: Caltech
Reminder : Transmission & Decentralized Trading BUS A BUS B G1 L2 G2 L1 L1 = 500, MC1= 10 + .01 P1, L2 = 1500, MC2 = 13 + .02 P2 A B 500 1500 Autarky a=15, b= 43 No Constraints
School: Caltech
Reminder : Transmission & Decentralized Trading BUS A BUS B G1 L2 G2 L1 L1 = 500, MC1= 10 + .01 P1, L2 = 1500, MC2 = 13 + .02 P2 A B 500 1500 Autarky a=15, b= 43 No Constraints
School: Caltech
demand response Power struggle: Green energy versus a grid that's not ready h8p:/www.la;mes.com/na;on/la- na- grid- renewables- 20131203 Caiso 2030 Variable resource Caiso 2020 at 30% renewables Balancing Act Implica;
School: Caltech
CS/EC 133 Electricity Markets Lecture 1 Introduc-on Slides by: Tom Overbye, University of Illinois With addi-ons by Ross Baldick, University of Texas And John Ledyard, Caltech Simple Power System Every
School: Caltech
nearest neighbors K h(x) = wk exp x k neural 2 networks k =1 SVM Kernel = RBF regularization k wk unsupervised learning
School: Caltech
nearest neighbors K h(x) = wk exp x k neural 2 networks k =1 SVM Kernel = RBF regularization k wk unsupervised learning
School: Caltech
Hi Hi Hi Hi zn n > 0 E[ ] E [E ] Hi xn Hi Hi = N 1 L() = n 2 n=1 N N ynym nm xnxm n=1 m=1 N 1 Hi h H N 1 L() = n 2 n=1 n 0 N Z N y n y m n m z zm n n=1 m=1 n = 1,
School: Caltech
E (h) E = (h) = E (h) + (h) N w w = 0.0001 E = 1.0 (w) = E (w) + N ww y ww = C y E x h x
School: Caltech
K (x, x) = zz Z 1 ww + C 2 N n n=1 Hi Hi violation Hi K (x, x) = exp x x Hi 2 0 n C (xn, yn) D h(x) x xn N wn exp x xn h(x) = n=1 2
School: Caltech
1 + + + + + + + + + + x2 1 x1 1 x 1 l L (l) xj = d s l = L (s) xd + + h (x ) (l1) (l) j (l ) wij = xi (l1) (l) wij i=0 (s) = tanh(s) (l1) xi d( l ) (l1) i (l) (l1) 2 = (1 (xi ) (l) wij j j =1
School: Caltech
x0 x1 s h(x) x2 xd E (s) w w(0) (ynwxn) P (yn | xn) = n=1 w(t + 1) = w(t) E (w(t) N N n=1 t = 0, 1, 2, w N 1 E (w) = N h(xn), yn n=1 ln(1+eynw xn )
School: Caltech
E gm D (N ) D E gm (N K ) g D D (K ) E (g ) E (g ) E(g ) K z g D | cfw_ D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 Hi
School: Caltech
d wixi = w x i=0 h(x) = (wx) h(x) = wx 1 w = (X X) X y y x1 x2 wx w x z (x1, x2) (x2, x2) 12
School: Caltech
g h 1 , h2 , , hM Hi |E (g ) E (g )| > Eout(h) |E (h1) E (h1)| > |E (h2) E (h2)| > |E (hM ) E (hM )| > Ein(h) Hi P[ 22N |E (h) E (h)| > ] 2e M
School: Caltech
d(H) 10 10 5 10 H 0 10 5 10 up 20 UNKNOWN TARGET FUNCTION f: X Y 80 100 120 140 160 180 200 N d DISTRIBUTION on X TRAINING EXAMPLES ( x1 , y1 ), . , ( xN , y ) N ALGORITHM 60 PROBABILITY P LEARNING 40 FINAL HYPOTHESIS g~f ~ A E HYPOTH
School: Caltech
mH(N ) H N 1 2 3 4 5 6 : 1 1 1 1 1 1 1 : Hoeffding Inequality Union Bound VC Bound k k 23456 22222 34444 4 7 top 8 8 8 5 11 . . . . . . 6: . 7: . : . bottom k1 mH(N ) i=0 . . . . . . . . . . N i N k1 space of data sets . D (a) [ |E (b) (c) [ |E
School: Caltech
y = f (x) h(x), f (x) 8 >+1 < > : 1 1 E (h) = N target function f: x) XY plus noise TRAINING EXAMPLES ( x1 , y1 ), . , ( xN , y ) N UNKNOWN INPUT DISTRIBUTION P (x) N h(xn), f (xn) n=1 (x1, y1), , (xN , yN ) E (h) = Ex P (x, y ) = P (x)P (y
School: Caltech
mH(N )= max x1, ,xN X |H(x1, , xN )| x1 x2 x3 mH(N ) mH(N ) M mH(N ) mH(N ) mH(N ) B (N, k ) N
School: Caltech
Course: CS 21
CS 21 Decidability and Tractability Winter 2012 Final Exam Solutions Posted: March 16 If you have not turned in the nal, obviously you should not consult these solutions. 1. (a) First, the problem is in PSPACE, for the usual reason for 2-player games. Giv
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Midterm Out: February 6 Due: February 13 This is a midterm. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Final Out: March 13 Due: March 20, noon This is a nal exam. You may consult only the course notes and the text (Sipser). You may not collaborate. The full honor code guidelines can be found in the course syl
School: Caltech
Course: Computation, Computers, And Programs
Quiz3 1. (10) Prove that equality i = j of partial recursive functions is undecidable. 2. (10) Show that the time-bounded while-programs are primitive recursive. The time-bounded programs are defined as follows. For any while loop while x y do e done, the
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Final Solutions Posted: June 10 Chris Umans 1. (a) The procedure that traverses a fan-in 2 depth O(logi n) circuit and outputs a formula runs in Li this can be done by a recursive depth-rst traversal, which only requir
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Midterm Solutions Posted: May 9 Chris Umans 1. Consider a language L coNEXP. On an input of length n, the advice will be an exact count of the number of inputs of length n not in the language. This is a number between
School: Caltech
make-inventory: inv: Result: 15 param: nil body: (let ) total: 0 -> 10 -> 15 items: 'pencils 'stapler param: op . args body: (cond ) op: 'add-item! args: (list 'stapler 10) op: 'add-item! args: (list 'pencils 5) op: 'total-value args: (list) Result: 15
School: Caltech
CS38 Midterm Exam May 4, 2012 1. Due no later than Friday May 11, 2012 at 5:00pm in the computer lab. 2. This exam is not timed, plan your work as is convenient to you. 3. You may use the following resources during the exam: your own notes, homework probl
School: Caltech
Course: Decidability And Tractability
CS 21 Decidability and Tractability Winter 2013 Final Exam Solutions Posted: March 20 If you have not turned in the nal, obviously you should not consult these solutions. 1. (a) This problem is in PSPACE. We give a recursive algorithm. We are given a sequ
School: Caltech
CS 151 Complexity Theory Spring 2011 Final Out: May 26 Due: 1pm June 2 This is a nal exam. You may consult any of the course materials and the text (Papadimitriou), but not any other source or person. There are 4 problems on three pages. Please attempt al
School: Caltech
CS 151 Complexity Theory Spring 2011 Final Solutions Posted: June 3 Chris Umans 1. (a) The procedure that traverses a fan-in 2 depth O(logi n) circuit and outputs a formula runs in Li this can be done by a recursive depth-rst traversal, which only require
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 First Assignment This assignment counts for 10% of the final grade. (late submissions lose 10 pts from the score, cumulatively each day at noon) Solutions are due: Noon, 22 January 2013 via email to gerard@spinroot.com (plain
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Second Assignment This assignment counts for 10% of the final grade. (late submissions lose 10 pts from the score, cumulatively each day at noon) Solutions are due: Noon, 29 January 2013 via email to gerard@spinroot.com (plain
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Third Assignment This assignment counts for 10% of the final grade. Solutions are due: Noon, 5 February 2013 (10 pts are deducted if submitted late, cumulatively each day at noon) via email to gerard@spinroot.com 1) (20 pts) C
School: Caltech
Course: Logic Model Checking For Formal Software Verification
Logic Model Checking, CS 118 Fourth Assignment This assignment counts for 10% of the final grade. Solutions are due: Noon, Thursday 14 February 2013 Reminder: there is no lecture on Tuesday February 12. (10 pts deducted if submitted late, cumulatively eac
School: Caltech
October 14, 2013 Ec/CS 133 Problem Set #1 revised Answers due Monday October 21 , 5 PM in box outside of my oce Baxter 102. Question 1 A company has 2 plants with which it can produce units of output. The cost functions 2 2 of the plants are C 1 (y1 ) = 1
School: Caltech
November 3, 2013 Ec/CS 133 Problem Set #2 Problems due Nov 13, in class. Question 1 There is a 3 bus power system. On node 1 there is a generator B and a 400 MW load. On node 2 there is a generator A and an 80 MW load. On node 3 there are 2 generators, C
School: Caltech
November 21, 2013 Ec/CS 133 Problem Set #3 Due date: Dec 4 (in class) We plan to have it graded by Dec 6 in class. Question 1 (Forward and spot markets) The California ISO has a service called convergence bidding. You can nd a description at http:/www.cai
School: Caltech
Course: Database
CS 121 HW6 Shupin Mao November 20, 2013 Problems 1 a) There is no functional dependency in this many-to-many relation since a can map to several b and b can also map to several a; b) b a because one b can only map to one a, so if b1 = b2 , then a1 = a2 ,
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Solution Set 1 Posted: April 11 Chris Umans 1. Let A be a language that is downward self-reducible. Given an input x, we simulate the polynomial-time computation that (with queries) decides A, and recursively compute t
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Solution Set 2 Posted: April 18 Chris Umans 1. Suppose L NP coNP. Then there exist languages R1 and R2 in P for which L = cfw_x : y, |y | |x|k1 , (x, y ) R1 L = cfw_x : z, |z | |x|k2 , (x, z ) R2 On input x, our stro
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Solution Set 3 Posted: April 25 Chris Umans 1. (a) Note: it is most convenient to think of as the permutation k ( (k ) rather than the more conventional k ( (k ) the two notions are equivalent by taking inverses; howev
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Solution Set 4 Posted: May 2 Chris Umans If you are turning in this problem set late, obviously you shouldnt consult these solutions. 1. Consider a language L ZPP decided by a machine M that runs in expected time nk fo
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Solution Set 5 Posted: May 16 Chris Umans 1. We are given a Boolean circuit C on n variables x1 , x2 , . . . , xn with m , and gates. Our 3-CNF formula will have m auxiliary variables z1 , z2 , . . . , zm in addition t
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Solution Set 6 Posted: May 23 Chris Umans 1. (a) We observe that the largest possible set shattered by a collection of 2m subsets is m, since a set of size m + 1 has more than 2m distinct subsets. The VC dimension of a
School: Caltech
Course: Complexity Theory
CS 151 Complexity Theory Spring 2013 Solution Set 7 Posted: May 30 Chris Umans Obviously, if you have not yet turned in Problem Set 7, you shouldnt consult these solutions. 1. (a) Let pi = Pry [f (x + y ) f (y ) = i]. The probability two random voters dis
School: Caltech
CS 151 Complexity Theory Spring 2011 A Sample LTEX Template March 27, 2011 (Your Name) 1. Please remember that homework solutions should be: Clear Concise Precise Legible (if handwritten). 2. An example1 : (Yes) According to the fundamental theorem of
School: Caltech
CS/EE 147 Assigned: 05/25/10 HW 7: Scheduling Guru: Raga Due: 06/04/10, Ragas mailbox, 1pm We encourage you to discuss these problems with others, but you need to write up the actual solutions alone. At the top of your homework sheet, list all the people
School: Caltech
CS/EE 147 Assigned: 05/13/10 HW 6: Transform world Guru: Lina Due: 05/26/10, Ragas mailbox, 1pm We encourage you to discuss these problems with others, but you need to write up the actual solutions alone. At the top of your homework sheet, list all the pe
School: Caltech
CS/EE 147 Assigned: 05/06/10 HW 5: Queueing networks and PH distributions Guru: Raga Due: 05/14/10, Ragas mailbox, 1pm We encourage you to discuss these problems with others, but you need to write up the actual solutions alone. At the top of your homework
School: Caltech
CS/EE 147 Assigned: 04/27/10 HW 4: Queueing games Guru: Lina Due: 05/07/10, Ragas mailbox, 1pm We encourage you to discuss these problems with others, but you need to write up the actual solutions alone. At the top of your homework sheet, list all the peo
School: Caltech
CS/EE 147 Assigned: 4/13/10 HW 3: Practice with CTMCs Guru: Raga Due: 4/28/10, Ragas mailbox, 1pm We encourage you to discuss these problems with others, but you need to write up the actual solutions alone. At the top of your homework sheet, list all the
School: Caltech
HW 2: Practice with DTMCs CS/EE 147 Assigned: 04/06/10 Guru: Lina Due: 04/16/10, Ragas mailbox, 1pm We encourage you to discuss these problems with others, but you need to write up the actual solutions alone. At the top of your homework sheet, list all th
School: Caltech
CS/EE 147 Assigned: 03/30/10 HW 1: Probability Refresher Guru: Raga Due: 04/09/10, Ragas mailbox1 , 1pm We encourage you to discuss these problems with others, but you need to write up the actual solutions alone. At the top of your homework sheet, list al
School: Caltech
Course: Computer Language Shop
C track: assignment 5 Goals In this assignment you will write a program to simulate a simple one-dimensional cellular automaton, which are related to (but are not the same as) two-dimensional cellular automata like Conway's game of Life. We will use this
School: Caltech
Course: Computer Language Shop
C track: assignment 8: Implementing a virtual machine Goals This lab is the last assignment in this track. By now you know almost all the important aspects of the C language, with the exception of a few features like function pointers which aren't really
School: Caltech
Course: Computer Language Shop
C track: assignment 7 Goals This week, we are going to move beyond a discussion of built-in features of the C language (we've covered most of them already) and continue discussing how to implement fundamental data structures in C. The data structure we wi
School: Caltech
Course: Computer Language Shop
C track: assignment 6 Goals In this assignment you will write a sorting program similar to the program from lab 3, except that it uses linked lists instead of arrays to hold the list of numbers read in off the command line. In the process, you will learn
School: Caltech
Fall 2013 Syllabus CS/EC 133: Electricity Markets Meets Wednesday- Friday: 1- 230 pm in Baxter 25. Instructor: John Ledyard Office: Baxter 102, x8482, Email: jledyard@caltech.edu, Office Hours:
School: Caltech
Course: Decidability And Tractability
CS21: Decidability and Tractability course information and tentative schedule Catalog description: This course introduces the formal foundations of computer science, the fundamental limits of computation, and the limits of ecient computation. Topics will
School: Caltech
CS 151 Complexity Theory Spring 2011 Course Summary and Syllabus Lecturer: Chris Umans Date: March 29 Course summary: Complexity Theory attempts to answer the question: What is computationally feasible given limited computational resources? In this course
School: Caltech
CS 9 Introduction to Computer Science Research Fall 2011 Course Summary and Syllabus Date: October 5 This course will introduce the research areas of the computer science faculty, through weekly overview talks by the faculty aimed at rst-year undergraduat