Fundamentals of Automata Theory

Automata theory underpins natural language processing, string processing, search engines, and lexical analysis in compilers, and introduces Chomsky hierarchy with finite automata, push-down automata, linear bounded automata, and Turing machines.

Define deterministic finite automata as a set of states with a single transition for each input symbol from the alphabet; illustrate with an on/off electric switch and delta, q0, F.

Design a dfa that accepts all strings over a and b ending with 'aa', using states q0, q1, q2 and the minimal string 'aa'.

Explain non-deterministic finite automata, which differ from deterministic automata by allowing zero, one, or more transitions per state, with the delta mapping to 2^Q and a and b examples.

Explore epsilon NFA concepts by allowing transitions on epsilon, and learn how to combine automata to accept even zeros or even ones.

Pushdown automata extend finite automata with a stack, making moves depend on input, stack top, and state to push or pop, enabling a raised to n b raised to n.

Design a pushdown automaton to accept the binary form w c w^r, pushing w before c and popping to verify the reverse after c.

Explore linear bound automata, a nondeterministic turing machine with left and right end markers, bounded by dollar one and dollar two, recognizing context-sensitive languages like a^n b^n.

A Turing machine is an automaton with a finite control and an input tape, reading and writing symbols as the tape head moves left or right, defined by a seven-tuple.