Formal Languages and Automata theory

Construct a deterministic finite automaton with three states representing remainders 0, 1, and 2; transition on each a advances the remainder; accept when the remainder is 0.

Explain how to design a deterministic finite automaton that accepts strings starting with a and ending with b, using states to enforce the initial a and final b.

Explore how a dfa recognizes the language a^n b^m with n,m >=1 by enforcing a's then nonempty b's, with no a after a b.

Learn how to build a dfa for the language a^n with n≥1 and n≠3, distinguishing lengths 0,1,2,3 and 4 plus to accept all valid lengths while rejecting 0 and 3.

Learn how to determine whether two DFAs recognize the same language by comparing their accepted and rejected strings through a joint state traversal; a mismatch in final status proves inequivalence.

Construct a push down automaton that accepts a^n b^n with n≥1 by pushing a's and popping on b's, using the bottom symbol and acceptance by final state or empty stack.

Design a pushdown automaton that accepts strings where the number of a's equals the number of b's, using a bottom marker, push and pop rules, and epsilon transitions.

Demonstrates constructing a pushdown automaton for the language a^n b^n c with n>=1, using push and pop on a and b, and validating a final c with the stack top.

Construct a pushdown automaton that accepts the language wcwR by pushing symbols until the marker c and then popping to match the reverse.

Design a nondeterministic pushdown automaton for the language L = { wwR }, identifying the middle point without a separator by pushing and popping on the stack.

Construct a pushdown automaton that accepts a^n b^{2n} over {a,b} by pushing two symbols for each a and popping one symbol for each b, ensuring 2n pushes match 2n pops.

Design a pushdown automaton that accepts a^n b^n a^m with m,n ≥ 1 over {a,b}, by pushing a's, popping on b's, and handling trailing a^m with a stack pivot.

Design a Turing machine for the language w c w^R, where w ∈ {a,b}*, showing how to match first and last symbols and verify the reverse after c.

Construct a Turing machine that accepts the language l = ww^R, where w = (a+b)*, by illustrating the mirrored structure and matching symbols with blanks.