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This is an introductory course on Theory of Computation intended for undergraduate students in computer science. In this course we will introduce various models of computation and study their power and limitations. We will also explore the properties of the corresponding language classes defined by these models and the relations between them. We will assume the student is comfortable in analytical reasoning and has preferably done a course on Data Structures and Algorithms.

 
Week

Topics

1.

Finite Automata – deterministic and nondeterministic, regular operations

2.

Regular Expression, Equivalence of DFA, NFA and REs, closure properties

3.

Non regular languages and pumping lemma, DFA Minimization,

4.

CFGs, Chomsky Normal Form

5.

Non CFLs and pumping lemma for CFLs, PDAs,  Equivalence of PDA and CFG

6.

Properties of CFLs, DCFLs, Turing Machines and its variants

7.

Configuration graph, closure properties of decidable languages, decidability properties of regular languages and CFLs

8.

Undecidability, reductions, Rice's Theorem, introduction to complexity theory

  1. Abstract Algebra: Theory and Applications by Thomas W. Judson, available as PDF at http://abstract.ups.edu/download/aata-20110810.pdf
  2. Abstract Algebra by I. N. Herstein


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