T.E. Sem.V [CMPN]
Theory of Computer Science
Time : 3 Hrs. Theory : 100 Marks Term Work : 25 Marks
Introduction : alphabets, Strings and Languages, automata and Grammars. Finite Automata (FA) −its behavior; DFA − Formal definition, simplified notations (state transition diagram, transition table), Language of a DFA. NFA−Formal definition, Language of an NFA. An Application : Text Search, FA with epsilon−transitions, Eliminating epsilon−transitions, Eliminating epsilon−transitions, Equivalence of DFAs and NFAs. Regular expressions (RE) − Definition, FA and RE, RE to FA, FA to RE, algebraic laws for RE, applications of REs, Regular grammars and FA, FA for regular grammar, Regular grammar for FA. Proving languages to be non−regular − Pumping Lemma, and its applications. Some closure properties of Regular languages − Closure under Boolean operations, reversal homomorphism, inverse homomorphism, etc. M hill−Nerode Theorem. DFA Minimization Some decision properties of Regular languages − emptiness, finiteness, membership, equivalence of two DFAs or REs, Finite automata with output. Context−free Grammars (CFGs) − Formal definition, sentential forms, leftmost and rightmost derivations, the language of a CFG. Derivation tree or Parse tree−Definition, Relationship between parse trees and derivations. Parsing and ambiguity, Applications of CFGs, Ambiguity in grammars and Languages. Simplification of CFGs − Removing useless symbols, epsilon−Productions, and unit productions, Normal forms −CNF and GNF. Proving that some languages are not context free −Pumping lemma for CFLs, applications. Some closure properties of CFLs − Closure under union, concatenation, Kleene closure, substitution, Inverse homomorphism, reversal, intersection with regular set, etc. Some more decision properties of CFLs, Review of some undecidable CFL problems. Pushdown Automata (PDA) − Formal definition, behavior and graphical notation, Instantaneous...
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