Module28 - Module 28 Context Free Grammars Definition of a...

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1 Module 28 Context Free Grammars Definition of a grammar G Deriving strings and defining L(G) Context-Free Language definition
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2 Context-Free Grammars Definition
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3 Definition A context-free grammar G = (V, Σ, S, P) V: finite set of variables (nonterminals) Σ: finite set of characters (terminals) S: start variable element of V role is similar to that of q 0 for an FSA or NFA P: finite set of grammar rules or production rules Syntax of a production variable string of variables and terminals
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4 English Context-Free Grammar ECFG = (V, Σ, S, P) V = {<sentence>, <noun phrase>, <verb phrase>, ... } people sometimes use < > to delimit variables In this course, we generally will use capital letters to denote variables Σ = {a, b, c, ..., z, ;, ,, ., ...} S = <sentence> P = { <sentence> <noun phrase> <verb phrase> <pct>, <noun phrase> <article> <adj> <noun>, ...}
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5 {a i b i | i>0} CFG ABG = (V, Σ, S, P) V = {S} Σ = {a, b} S = S P = {S aSb, S ab} or S aSb | ab second format saves some space
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6 Context-Free Grammars Deriving strings, defining L(G), and defining context-free languages
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