Formal Language and Automata: CFG, PDA and TM

Explore pushdown automata, an epsilon-NFA with a stack, and seven-tuple framework, detailing stack operations and delta transitions; it shows a pda for zero-to-n and one-to-n with final-state and empty-stack acceptance.

Constructs a PDA for the language a^n b^{2n} with n≥1, using the stack to push a's and pop for b's, and accepts by final state.

Construct a pushdown automaton that recognizes a^n b^m c^n with n, m ≥ 1 by pushing each a, leaving the stack unchanged for b's, and popping for each c.

Learn to construct a pushdown automaton for a^n b^m c^m d^n by pushing A and B, then matching C with B and D with A, ending with an empty stack.

This lecture presents nondeterministic PDAs for the language w w^r, shows pushing the first half onto the stack and popping the second half, with epsilon transitions deciding the split.

Demonstrate how a deterministic PDA converts a nondeterministic PDA for w c w reverse by inserting C, pushing the first half, then popping the second; illustrate with a^n b^n.

Convert a context-free grammar to a pushdown automaton that accepts by empty stack, detailing states, stack symbols, terminals, and transition rules, with an example.

Learn to convert a pushdown automaton to a context-free grammar by building CFG variables from PDA states and stack symbols and deriving productions from transitions.

Explain the pumping lemma for context-free languages, use a contradiction to show a language is not CFL, and apply it to the example a^n b^n c^n.

Apply pumping lemma for CFLs to show a language is not CFL, using five-way split u v w x y and i = 0 to obtain a string outside L.

Learn to construct a Turing machine that concatenates unary strings of m zeros and n zeros using a separator symbol, with left and right moves culminating in a final state.

Demonstrates a turing machine that accepts a^n b^n c^n by marking a with x, b with y, c with z and performing left-right sweeps to verify equality.

Design a Turing machine to accept palindromes over 0 and 1 by matching first and last symbols, replacing matches with blanks, and reaching the final accept state.

Construct a Turing machine that accepts strings containing the substring 010, using states q0 to q4 and tape symbols 0, 1, and blank, and accept upon reaching q4.

Design a Turing machine to perform subtraction: compute m−n when m>n, erase the tape for m≤n, and handle m=n cases with zeros, a separator, and blanks.

Learn to design a Turing machine that multiplies m and n via repeated addition. Load m zeros, one, and n zeros to produce m×n on the tape.

Storage in finite control stores information as a pair: a state and the scanned symbol. The lecture uses a Turing machine example to illustrate transitions and swapping a and b.

Explore non deterministic Turing machines with a finite control and a single one-way infinite tape, where multiple next moves may occur, unlike deterministic TMs.

Explain multi-tape Turing machines with finite control and multiple infinite tapes, each tape with its own initial and accepting states, an input on the first tape, and head movements.