The following is a grammar for regular expressions over symbols a and b only, using + in place of 1 for union, to avoid conflict with the use of vertical bar as a metasymbol in grammars: a) Left factor this grammar. b) Does left factoring make the grammar suitable for top-down parsing? c) In addition to left factoring, eliminate left recursion from the original grammar. d) Is the resulting grammar suitable for top-down parsing?

The following is a grammar for regular expressions over symbols a and b only, using + in place of 1 for union, to avoid conflict with the use of vertical bar as a metasymbol in grammars: a) Left factor this grammar. b) Does left factoring make the grammar suitable for top-down parsing? c) In addition to left factoring, eliminate left recursion from the original grammar. d) Is the resulting grammar suitable for top-down parsing?

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter12: Adding Functionality To Your Classes

Section12.5: Virtual Functions

Problem 4E

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Question

The following is a grammar for regular expressions over symbols a and b only, using + in place of 1 for union, to avoid conflict with the use of vertical bar as a metasymbol in grammars:

a) Left factor this grammar.

b) Does left factoring make the grammar suitable for top-down parsing?

c) In addition to left factoring, eliminate left recursion from the original grammar.

d) Is the resulting grammar suitable for top-down parsing?

rexpr
rterm
rfactor
rprimary
→>> rexpr + rterm | rterm
rterm rfactor | rfactor
→> rfactor * | rprimary
a/b

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