CSE860 Final Due: Saturday 12 noon, May 1. PART I. Solve problem 1 and 2. 1. For each of the following assertions, state whether they are True, False, or Open according to our current state of knowledge of computability and complexity theory, as desc
CSE860 Exam
Due: 5 pm March 19.
PART I. Solve the following three problems.
1. Suppose that
(i)
A and B are problems in P,
(ii)
C and D are in NP,
(iii) E is NP-complete.
(iv)
F is co-NP.
For each of the following questions, answer either
"false" (i.e., n
CSE860 HW 4. Due: April 23, 5pm
1. Solve 7.28 2. Solve 8.5 3. Solve 8.12 4. Solve 8.20 5. Solve 9.9 6. Solve 9.18 7. Show that if NP is a subset of BPP, then RP = NP.
RELATIVIZATION
CSE860 Vaishali Athale
Overview
Introduction Idea behind "Relativization" Concept of "Oracle" Review of Diagonalization Proof Limits of Diagonalization method
Proof idea Proof Implications of proof
Introduction
Revisiting qu
Computer Science 860 Foundations of Computing
Spring, 2004
Instructor: Moon Jung Chung chung@cse.msu.edu Office Hours: Tu, Th 1-2pm&by appointment Text: Introduction to the Theory of Computation by Michael Sipser Reference:
Computers and Intractabil
Week 4
Reduction via the history of Computation:
Linear Bounded Turing Machine (Automata)
Definition:
A linear bounded automaton is a restricted type of Turing machine where in the
tape head isn’t permitted to move off the portion of the tape containing t
PRIMES is in P
Manindra Agrawal Neeraj Kayal Nitin Saxena Department of Computer Science & Engineering Indian Institute of Technology Kanpur Kanpur-208016, INDIA Email: {manindra,kayaln,nitinsa}@iitk.ac.in
Abstract We present an unconditional deter
Probabilistic Algorithms Michael Sipser Presented by: Brian Lawnichak
Introduction
Probabilistic Algorithm
uses the result of a random process "flips a coin" to decide next execution
Purpose
saves on calculating the actual best choice avoids
Week 1:
Lecture 1
1.
Languages, Machines, Functions
2.
Languages
Regular Languages,
Context Free Language
Context Sensitive Languages
Recursively Enumerable Languages
How to define?
Grammars: Regular Grammars, CFG, CSG etc.
Grammar G = (V, Σ, P, S), where
CSE860 HW 2. Due Feb. 17 1. Construct "and-or" graph for the following CFG G and Using this graph, decide (i) if L(G) is empty or not, and (ii) if L(G) is finite or not. G: S -> AB| CA B -> BC | AB A -> a C -> aB | b 2. Solve 3.6 3. Solve 3.7 4. Solv
Week 2: Lecture 3 TM: tape: two way, can write. Formally, Turing machine M is a 7-tuple, (Q, , , , q0, qaccept, qreject,), where 1. 2. 3. 4. 5. 6. 7. Q is the set of states is the input alphabet not containing the special blank symbol is the tape alp
Week 3:
Some undecidable
1.
2.
ATM = {<M,w> | M is a TM and M accepts w} is undecidable.
ATM is Turing recognizable (recursively enumerable).
Diagonalization Method
Countable, uncountable
Z is countable, Z×Z is countable.
Theorem: A is a subset of B, and