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Chapter 0: Q55P (page 1)

Let G1 be the following grammar that we introduced in Example

2.45. Use the DK-test to show that G1is not a DFG.
R鈫�S|T

S鈫�aSb|ab

T鈫�aTbb|abb

Short Answer

Expert verified

Using the DK-test, it can be shown that G1is not a DFG.

Step by step solution

01

Explain DK-test

DK-test, is the procedure that determine that context-free grammar is

deterministic. DK is constructed in association with DFA and it accepts the

input if the input x satisfies the following conditions,

1. x is the prefix of some valid string v=xy

2. x ends with a handle of v .

02

Convert the CFG G to an equivalent PDA

Consider the grammar G1,


The language of the grammar is

,where A=and. Consider the string,and underline the handle as

follows,

aaabbb

aaSbb


asb


The leftmost reduction of the string aaabbbbbb , is as follows

aaabbbbb


aaTbbbb

aTbb

T

R

In the above two strings, the left most reduction alone was able to done. Hence, the

strings are unequal.

Therefore, form the above result, the condition of DK-test has been violated. Thus,

the grammar G1 is not a DFG.

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Most popular questions from this chapter

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Use the procedure described in Lemma 1.60to convert the following finite automata to regular expressions.

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