We have a grammar for simple arithmetic expressions E→E+F|F | E F→ F*T T T→a | e a) Grammar is ambiguous. Prove it! b) Modify this grammar to generate only valid arithmetic expressions with + operationsand. Grammar should be unambiguous. In this grammar you will find the derivation trees for the expressions E1:a + a* a +a+a* a E2: a* a *a+a* a c) We want to introduce the operator into the expressions, which must have a precedence higher than + but lower than *. For example, if the expression a*aa+a is enclosed in parentheses, the expression would be expressed as follows: ((a a) a)+a. Write down a grammar that generates such expressions and is unambiguous (add/modify as appropriate)the grammar defined above to get the correct result).

We have a grammar for simple arithmetic expressions E→E+F|F | E F→ FT T T→a | e a) Grammar is ambiguous. Prove it! b) Modify this grammar to generate only valid arithmetic expressions with + operationsand. Grammar should be unambiguous. In this grammar you will find the derivation trees for the expressions E1:a + a a +a+a* a E2: a* a a+a a c) We want to introduce the operator into the expressions, which must have a precedence higher than + but lower than . For example, if the expression aaa+a is enclosed in parentheses, the expression would be expressed as follows: ((a a) a)+a. Write down a grammar that generates such expressions and is unambiguous (add/modify as appropriate)the grammar defined above to get the correct result).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

We have a grammar for simple arithmetic expressions
E→E+FFE
F→ F*T T
T→a | e
a) Grammar is ambiguous. Prove it!
b) Modify this grammar to generate only valid arithmetic expressions with + operationsand.
Grammar should be unambiguous. In this grammar you will find the derivation trees for the expressions
E1:a + a *a +a+a*a
E2: a* a *a + a* a
c) We want to introduce the operator into the expressions, which must have a precedence higher than + but lower
than *.
For example, if the expression a*aa+a is enclosed in parentheses, the expression would be expressed as follows:
((aa).a)+a.
Write down a grammar that generates such expressions and is unambiguous (add/modify as appropriate)the grammar
defined above to get the correct result).

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