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CPSC 121: Models of Computation
2010 Winter Term 2
Introduction to Induction
Steve Wolfman
1
Outline
Prereqs, Learning Goals, and Quiz Notes
Problems and Discussion
Single-Elimination T
Lecture 6:
Universal TM and Nondeterministic TMs
Valentine Kabanets
September 19, 2013
1
Universal Turing machine
Turing (1936) showed that there exists a machine U that, when given as input (appropri
Lecture 7:
Decidable and semi-decidable languages, the Halting problem
Valentine Kabanets
September 24, 2013
1
N P and P
Recall that an NTM M is said to halt on an input x i all of its computation bra
Lecture 3:
Nondeterministic Finite Automata
Valentine Kabanets
September 11, 2013
1
Nondeterministic Finite Automaton (NFA)
Informally, an NFA has more than one option for the next transition. For exa
Lecture 14:
P , N P , and search to decision reductions
Valentine Kabanets
October 22, 2013
1
Complexity Theory
We take a closer look at the class of decidable problems, and want to classify these pro
Lecture 12:
Im not provable
Valentine Kabanets
October 10, 2013
1
Second Proof of Gdels First Incompleteness Theorem
o
Here we give another proof of Gdels First Incompleteness Theorem. In this proof,
Lecture 16:
NP-complete versions of SAT
Valentine Kabanets
October 29, 2013
1
NP-complete versions of SAT
We showed last time that SAT is NP-complete, where SAT is to decide if a given propositional
f
Lecture 13:
Gdels Second Incompleteness Theorem, and Tarskis Theorem
o
Valentine Kabanets
October 15, 2013
1
1.1
Gdels Second Incompleteness Theorem
o
Consistency
We say that a proof system P is consi
Lecture 20:
Randomized complexity
Valentine Kabanets
November 12, 2013
1
Randomized complexity classes
A language L RP if there is a deterministic polytime TM M (x, r) such that
1. for all x L, Prr [M
Lecture 19:
NL=coNL
Valentine Kabanets
November 7, 2013
1
N L-completeness
To talk about N L-completeness, we need to rene our notion of a reduction. Well talk about
logspace-computable reductions (re
Lecture 10:
Applications of the Recursion Theorem
Valentine Kabanets
October 3, 2013
1
Care with mapping-reductions
In class, we argued that the language ET M = cfw_ M | L(M ) = is undecidable. We pr
Lecture 24:
Overview
Valentine Kabanets
November 28, 2013
1
Computability
simple model of computation: Finite Automaton (FA)
variant: DFA = NFA , accept regular languages; can be represented also by
Lecture 8:
Rices Theorem
Valentine Kabanets
September 26, 2013
1
Another example of undecidability
Theorem 1. The language
EQT M = cfw_ M1 , M2 | L(M1 ) = L(M2 )
is undecidable.
Proof. Suppose it is d
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CPSC 121: Models of Computation
2011 Winter Term 1
Number Representation
Steve Wolfman, based on notes by
Patrice Belleville and others
1
Outline
Prereqs, Learning Goals, and Quiz Notes
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CPSC 121: Models of Computation
2011 Winter Term 1
Number Representation
Steve Wolfman, based on notes by
Patrice Belleville and others
1
Outline
Prereqs, Learning Goals, and Quiz Notes
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CPSC 121: Models of Computation
2009 Winter Term 1
Sequential Circuits (Mealy Machines)
Steve Wolfman, based on notes by
Patrice Belleville and others
1
Outline
Prereqs, Learning Goals, a
Mei Qin Chen
citadel-math231
WeBWorK assignment number Homework16 is due : 10/28/2011 at 10:00am EDT.
The
(* replace with url for the course home page *)
for the course contains the syllabus, grading
Lecture 15:
NP-completeness
Valentine Kabanets
October 24, 2013
1
Polytime mapping-reductions
We say that A is polytime reducible to B if there is a polytime computable function f (a reduction)
such t
Lecture 18:
PSPACE
Valentine Kabanets
November 5, 2013
1
Determinism vs. Nondeterminism
We have looked at the P vs. NP question, which is basically a question whether nondetemrinism
can be eciently re
Lecture 5:
Pumping Lemma, variants of Turing machines
Valentine Kabanets
September 17, 2013
1
Non-regular languages
Consider the language L = cfw_0n 1n | n 0. Intuitively, L cannot be accepted by any
Lecture 9:
Mapping reductions, and the Recursion Theorem
Valentine Kabanets
October 1, 2013
1
Reductions
We will consider a special kind of reductions: mapping reductions.
Denition 1. Language A is m-
Lecture 4:
Regular expressions versus Finite Automata
Valentine Kabanets
September 12, 2013
1
Regular expressions
We have the following inductive denition of regular expressions.
The following are re
Lecture 11:
Applications of Computability Theory: Randomness and Logic
Valentine Kabanets
October 14, 2013
1
Kolmogorov Complexity
Usually, when we say that a string x is random, we have some probabil