CS8813: Formal Languages and Automata Theory

• Background Information
• Basic proof concepts, induction, recursive construction
• Definitions of Languages, and how problems can be expressed in terms of defining Languages.
• Finite Automata and Regular Expressions
• Equivalence proofs for Deterministic, Non-Deterministic Finite Automata and Regular Expressions
• Definitions of Regular Languages
• Constructions for translating between different descriptions of Regular Languages.
• Properties of Regular Languages including closure under operations such as concatenation, union, etc.
• Minimization of automata transition functions.
• Context-Free Grammars and Languages
• Definition of grammars through production rules
• Parse Tree's and application to parsers
• Ambiguity in grammars and languages
• Identification of inherently ambiguious languages
• Definition of Pushdown Automata and proofs of equivalence to Context-Free Grammars.
• Proofs of distinctions between Regular Languages and Context-Free Grammars and languages defined by deterministic push-down automta.
• Proofs about Simplifying Context-Free Grammars: THe Chomsky Normal Form and Greibach Normal Form
• Techniques for Proving Languages are/are not described by context-free grammars.
• Proofs about closure properties of Context-Free Grammars under various operations (complement, union, intersection, etc.)
• Turing Machines
• The Halting Problem.
• Equivalences of deterministic and non-deterministic Turing Machines
• Equivalences of certian restricted forms of Turing Machines
• Relationship between a turing machine and a modern computer architecture
• Undecidability (Languages for which the turing machine cannot be guaranteed to terminate on failure.)
• Languages not recognized by Turing machines.
• diagonalization language
• Languages that are recognized by Turing machines but are undecidable.
• The Universal Turing Machine and the Universal Language
• Undecidability of the Universal Language
• Post's Correspondence Problem and other examples of undecidability
• Intractable Problems (Languages for which cannot be recognized efficiently)
  • Problems in the class of Deterministic and Non-Deterministic Polynomial time.
  • Polynonial-Time Reductions as a technique for proving that a problem is intractable.
  • NP-Complete Problems
  • The Satisfiability Problem