Theory of Computation
20 articles in this topic
Chomsky Hierarchy for GATE: Classifying a Grammar as Regular, Context-Free, Context-Sensitive or Type-0
Classify grammars mechanically from their production forms. Four worked boundary cases show exactly when a grammar moves from regular to CFG, CSG or Type-0.
Rice's Theorem for GATE: The Mechanical Test for Undecidability Questions
Run the semantic and non-trivial checklist on six machine properties, learn when Rice is silent, and separate undecidable from RE or non-RE.
NFA to DFA Conversion for GATE: Subset Construction and State-Count Numericals
Convert two small NFAs into complete DFAs, handle epsilon-closure and the dead state, and separate the reachable state count from the 2^n worst case.
Ambiguous Grammars, Precedence and Associativity for GATE: Two-Tree Proofs and Grammar Rewrites
Proving a grammar ambiguous takes one witness string and two parse trees. Removing the ambiguity takes precedence layers plus a chosen recursion direction.
DFA Minimization for GATE
Remove unreachable states, split final from non-final states, and refine until every transition signature is stable. A complete six-state example shows each split.
Turing Machines and Decidability: recursive vs RE, and the halting problem
Turing machines and decidability explained: TM definition and configurations, recursive vs recursively enumerable languages, the halting problem, reductions.
Context-Free Grammars and Pushdown Automata: CFGs, PDAs, and a worked example
Context-free grammars and pushdown automata explained: derivations, ambiguity, CNF and GNF, PDA acceptance modes, the pumping lemma, and a worked example.
Finite automata: DFA vs NFA, with the exam angle
Finite automata explained: the DFA and NFA 5-tuple, DFA vs NFA, a worked subset construction converting an NFA to a DFA, equivalence, and the exam angle.