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Introduction The Turing Machine (TM) was proposed by Alan Turing (1936). Definition A Turing Machine is an abstract machine or theoretical computational model that manipulates symbols on an infinite tape according to a set of rules. A Turing Machine is defined in a 7-tuple …

Introduction A Push-Down Automata (PDA) is a type of automaton (abstract machine) used in the theory of computation.  Definition Pushdown automata are an abstract computational model that uses a stack to recognize context-free languages. A Push-Down Automaton is a finite …

Introduction A Context-Free Grammar (CFG) is a formal system that provides a precise way to define valid strings in a language. Definition A Context-Free Grammar (CFG) is a formal grammar used to define context-free languages, where each production rule has …

Introduction The Pumping Lemma states that every regular language has a pumping length such that sufficiently long strings can be decomposed and repeated while remaining in the language. Definition The Pumping Lemma is a powerful theoretical tool that helps identify …

Introduction A language is regular if and only if it can be accepted by a finite automaton. Finite Automata (FA) is the simplest computational model/abstract machine in the Theory of Computation (TOC). Finite Automata form TOC’s base, and are extended …

Language(L) A language is the set of all the strings of length exactly they have over a finite alphabet (Σ). A language is strings with grammar. Alphabets used in a language may be English, Hindi, or others. A language includes …

History The concept and roots of TOC originated in the 1930s/early 20th century during the “Crisis in Foundations of Mathematics,” when pioneering logicians like Kurt Gödel, Alonzo Church, and Alan Turing independently tackled Hilbert’s Entscheidungsproblem (decision problem).  Modern TOC started …