CSE599 Lecture2: Theoretical Background
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Table of Contents
Week 2: Theoretical Background
Introduction
History
A Model of Computation
Applicability
Applicability (cont.)
A First Model for Computation: Automata
Automata
Automata- Examples
More Complicated Example
Language
Limitations of DFA’s
Nondeterminism
NFA Example
NFA’s and DFA’s are equivalent!
DFA’s vs. Computers
Turing Machines
Turing Machines
A Definition of Algorithm
Relation to Other Models
More on Turing Machines.
Turing Machines
Turing Machines
Turing Machines
Back to the big questions
Recognizable
Decidable
Decidable
The idea of Universal Turing Machines.
ACC is Undecidable
Corollary: HALT is undecidable
Corollary: DOESN’T-HALT is unrecognizable
Discussion
Sidelight: Gödels Thrm
Alternate Models of TMs
More Powerful Models
Time and Space
Polynomial Time
The Class NP
Verifiers
NTM can answer NP problems in polytime.
NP Hard, NP Complete
Cook-Levin: SAT is NP complete
SAT is NP complete (cont.)
Reductions
PSPACE
NPSPACE
HIERARCHY
Applicability
Ill-posed problems
Unanswered questions
Representation
Model vs. Implementation
Author:
Erik Vee
Email:
env@cs.washington.edu
Home Page:
http://www.cs.washington.edu/education/courses/599/99sp/