hw6cs - CSE 105 Introduction to the Theory of Comptuation...

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Unformatted text preview: CSE 105: Introduction to the Theory of Comptuation Fall 2010 Problem Set 6 Instructor: Daniele Micciancio Due on: Fri. Nov 19, 2010 Problem 1 Consider a context free grammar G over the alphabet { , 1 } . Any such a grammar can be described as a string of symbols (very much like computer programs can be stored in text files) over the alphabet Σ = { , 1 ,A, [ , ] ,>, ; } , where grammar variables are represented as elements of an array A [ n ] . For example, the grammar A 1 → A 1 1 A 1 → A 2 A 2 → A 2 A 2 → can be represented by the string “A[1]>0A[1]1;A[1]>A[10];A[10]>0A[10];A[10]>;”. (The index of the array is represented in binary notation, and by convention, the start symbol of the grammar is the left hand side of the first rule in the grammar description. Also, the empty string is considered a valid CFG with no rules.) Prove that the set of all context free grammars as described above is regular by giving a DFA M for it....
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