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Finite state automata and regular expressions. Context-free grammars and pushdown automata. Turing machines. Models of computable functions and undecidable problems. The course emphasis is on the theory of computability, especially on showing limits of computation. May be taken for graduate credit.

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Introduction to the Theory of Computation

  1. finite automata
  • Deterministic Finite Automata
  • Non-Deterministic Finite Automata
  • Finite Automata with Epsilon-Transitions
  • Formal Notation for Epsilon-NFAs
  • Epsilon-Closure
  • Extended Transistions and Languages for Epsilon-NFAs
  • Eliminating Epsilon-Transitions
  1. regular expressions
  • Finite Automata and Regular Expressions
  • Algebraic Laws of Regular Expressions
  • The Pumping Lemma
  • Closure Properties of Regular Languages
  1. Context-Free Grammars
  • Definition
  • Parse Trees
  • Ambiguity in Grammars and Languages
  1. Pushdown Automata
  • Definition
  • Languages of PDA
  1. Context-Free Languages Equivalence of PDAs and CFGs
  • Chomsky Normal Form for Context-Free Grammars
  • Closure Properties of Context-Free Languages
  • Decision Problems for CFLs
  1. Turing Machines
  • Definition
  • Undecidability
  • Undecidable Problems about Turing Machines
  • Post's Correspondence Problem
  1. Intractable Problems
  • P and NP Classes
  • The SAT problem
  • Restricted SAT problems
  • Independent Sets
  • Directed Hamiltonian-Circuit
  • Undirected Hamiltonian-Circuit
  • Traveling Salesman Problem

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Finite state automata and regular expressions. Context-free grammars and pushdown automata. Turing machines. Models of computable functions and undecidable problems. The course emphasis is on the theory of computability, especially on showing limits of computation. May be taken for graduate credit.

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