Theory of Automata and Computation

Explore the building blocks of formal languages: alphabets, strings, and words, and see how concatenation and rules define a language, with examples using a, b and 0,1.

Examine the empty string, length of string, and reverse of string, and define the power of an alphabet and the power of a string with concrete examples.

Explore practice problem on S* with S = {a, b}, showing there are 2^2 words of length 2, 2^3 words of length 3, and 2^n words of length n.

Explore kleen star and kleen plus operators, including the empty string and positive closure, and learn lexicographic order in formal language theory.

Clarify the difference between formal syntactic languages and informal semantic languages, focusing on rules over meanings, to build core concepts in automata theory.

Explore descriptive definitions of formal languages and palindrome language, where strings equal their reverse, with examples like Λ, a, aba, and bb.

Explore the recursive definition of languages, defining positive even integers and palindrome language through simple rules. Learn how base objects, construction rules, and exclusivity determine the set.

Explore regular expressions, learning how to define languages using power, concatenation, and union, with examples like a*, a+, ab*, a+b, (a+b)*, and a(a+b)*a.

Define and manipulate regular expressions to capture substrings within languages. Solve examples showing how powers, concatenation, union, and Kleene star produce patterns that include or exclude specific substrings.

Learn to construct regular expressions for even-even languages, such as even number of a's and b's, and extend to even 0's and 1's, using union, concatenation, and Kleene star.

Explore finite automata as a graphical method to define languages, i.e., a finite state machine with five components: Q, Qo, F, Σ, and δ.

Explore DFA states—dead or trap, accepting, rejecting—and jump back, with examples of strings over {a,b} starting with a and prefixes like xy.

Construct DFA for languages that end with or start with a substring using type-01 and type-02 methods with solved examples, including state counts.

Explore how a transition graph defines a language, supporting multiple initial or final states, no dead states, and multiple transitions per symbol, as shown for the regular expression b*(a+b).

Compare regular languages, definable by regular expressions and recognized by finite state machines, with non-regular languages that require memory and counting, illustrated by a^n b^n and the ababbababb pattern.

Explore context-free grammar and language, including terminals, non-terminals, start symbol, and production rules, with examples deriving a^6 and (a+b)*, and relate CFLs to pushdown automata and programming syntax.

Explore pushdown automata, a finite state machine with a stack as infinite memory; understand its three components: input tape, control unit, and stack, and how push and pop govern acceptance.

Describe the formal definition of pushdown automata and its seven-tuple (Q, Σ, 𝜏, δ, q0, z0, F), and explain δ’s role in stack updates including pop, unchanged, and push.

Explore how to graphically represent pushdown automata with transition diagrams, interpret input symbols, stack top symbols, and ε moves, and design a non-deterministic PDA for the 0^n1^n language.

Design a pushdown automaton that accepts even palindromes of the form ww^R over {a,b}, pushing the first half and popping for the second half, with epsilon transitions at the midpoint.

Learn how the Turing machine extends finite automata and pushdown automata with an infinite tape, tape head, and deterministic transitions to recognize recursively enumerable languages.

Define a Turing machine as a seven-tuple (Q, Σ, τ, δ, q0, b, F), including states, input and tape symbols, the transition function, blank symbol, and accept or reject conditions.

Design a deterministic Turing machine to recognize the languages 01*0 and 0^N1^N, using a tape with x and y to mark processed symbols and an accept state.