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CS 3240: Languages and Computation. Context-Free Languages. Context-Free Languages. A single step derivation “ ” consist of the substitution of a variable by a string according to a substitution rule in R
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CS 3240: Languages and Computation Context-Free Languages
Context-Free Languages • A single step derivation “” consist of the substitution of a variable by a string according to a substitution rule in R • Note that rules use single arrows “”, while derivations themselves use double arrows “” • A sequence of several derivations (or none) is indicated by “ * ” • Previous example: “S * aabbaa” • L is a Context Free Language if and only if there is a context free grammar G=(V, Σ, P, S) such that L = L(G) = { w | w Σ * and S * w }
Some Remarks • The language L(G) = { w | w Σ* and S * w } contains only strings of terminals, not variables. • Notation: We can agglomerate several rules for one variable:A B A 01 by A B | 01 | AAA AA • What is the CFG ({S},{(,)},P, S) that produces the language of correct parentheses like (), (()), or ()(())? • Answer: S→ (S) | SS |