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Algebraic Expressions Via Arithmetic Operators

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Here is a context-free grammar that can be used to generate algebraic expressions via the arithmetic operators (addition, subtraction, multiplication, and division), in the variables p, q, and r. The letter E stands for expression;Rule 1: E ?? p;Rule 2: E ?? q;Rule 3: E ?? r;Rule 4: E ?? E + E;Rule 5: E ?? E ? E;Rule 6: E ?? E X E;Rule 7: E ?? E/E;Rule 8: E ??(E);(i). Use the above grammar to derive the string given by the mathematical expression E = (p + q) X p ? r X p/(q + q);(ii). Provide a parse tree for this derivation.

 

Paper#67545 | Written in 18-Jul-2015

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