Automata Theory

Mathematical Principles & Theorems

Models Deterministic Finite Automata (DFA) \(M = (Q, \Sigma, \delta, q_0, F)\) where \(Q\) is states, \(\Sigma\) is alphabet, \(\delta: Q \times \Sigma \to Q\) is transition function, \(q_0\) is start state, and \(F \subseteq Q\) is accept states. Kleene's Theorem establishes equivalence between DFAs, Non-Deterministic Automata (NFA), and Regular Expressions. The Pumping Lemma proves non-regularity by stating \(\forall s \in L\) with \(|s| \ge p\), \(s = xyz\) with \(|xy| \le p, |y| > 0\) such that \(xy^i z \in L, \forall i \ge 0\).

Operating Instructions

• Select an automaton preset (e.g., Even binary numbers, Alternating bits, Substring search) or construct custom states.
• Enter an arbitrary test string in the input field.
• Use 'Step' to step through transitions one symbol at a time or 'Run' to evaluate total acceptance.
• Watch active state nodes highlight on the interactive graph canvas and review transition history.