Theory of Automata | Formal Language and Automata Theory

Learn to design deterministic finite automata (DFA) that accept languages by defining transitions for every input, with a single initial state and at least one final state.

Apply Adam's theorem to convert a DFA to a regular expression, assuming no epsilon moves and a single initial state. Derive state equations from the DFA and solve them with q p* to obtain the final regular expression, using epsilon elimination and stepwise substitution.

Understand formal grammar as rules to generate syntactically correct strings, explore the Chomsky hierarchy from type 3 to type 0, and define terminals, nonterminals, start symbol, and productions.

Explore context free grammar, its A derives alpha productions with a single left-hand side, and how derivation trees show S generating palindromes and epsilon-based strings.

Explore left linear and right linear grammars and how to convert a left linear grammar into a right linear one via finite automata, state interchange, and reversed transitions.

Convert right linear grammar to left linear grammar by transforming to finite automata, swapping initial and final states, reversing transitions, and constructing the corresponding regular grammar.

Identify generating symbols and remove non generating symbols to obtain a reduced grammar. Then detect reachable and unreachable symbols to further simplify the grammar.

Identify nullable variables in a context-free grammar and systematically remove epsilon productions by generating new productions that include or exclude nullable symbols, preserving the language.

Eliminate unit productions from grammars by replacing a derives b with a derives alpha when b derives alpha, reducing extra steps in derivations.

Explore Greibach normal form, its relation to Chomsky normal form, and context-free grammar conversion steps. Eliminate null and unit productions, remove left recursion, and enable direct pushdown automaton recognition.

Learn how pushdown automata extend finite automata with a stack to recognize context-free languages, via the 7-tuple definition, stack operations, and two acceptance methods.

Explore pushdown automata that accept languages like a^n b^n c^m and its variants, using a stack to count a's, match with b's, and manage c's with transitions.

This lecture shows a pushdown automaton for the language a^(m+n) b^n c^m with m,n≥1, using a stack to push a’s and pop on b’s and c’s, accepting by empty stack.

Construct pushdown automata to accept a^{2n} b^{n} and a^{n} b^{2n} by pushing A for each A and popping for B, using epsilon transitions and state transitions.

Construct a pushdown automaton that accepts the language w, c, w by pushing w's symbols, reading c, and then popping to verify the reverse.

Explore the equivalence of context-free grammars and pushdown automata by constructing a PDA from a grammar using leftmost derivation and Greibach normal form, to recognize the generated language.

Construct a context-free grammar from a given pushdown automaton by deriving variables from states and stack symbols and translating transitions into productions with a matching start symbol.

Explore how a deterministic Turing machine, defined by seven tuples, reads binary input and accepts or rejects strings that begin or end with one.

designs a turing machine that accepts 1 0* 1 strings, showing turing machines can recognize regular languages, and demonstrates a 0^n 1^n check using marks X and Y.

The lecture designs a Turing machine over zero and one that accepts substring zero one, with any zeros and ones before and after, using x and y marks.

Learn how subroutines enable a Turing machine to multiply two integers on a zero–one tape by copying operands and reusing a repeated routine across iterations.

Explore the universal Turing machine by encoding a TM and its input in binary. A universal language is a Turing recognizable binary set that may accept, reject, or loop.

Explore decidability and undecidability through Turing machines, halting, and the distinctions between recursive, recursively enumerable, and decidable languages.

Explore the halting problem in Turing machines, showing that no algorithm can decide all programs' halting behavior. Understand why this undecidability follows from the Turing thesis and computability limits.