Let Sigma = {0,1} Show that { G is a CFG over {0,1} and 1 L{(G)

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Let Sigma = {0,1}. Show that { | G is a CFG over {0,1} and

1* L{(G) 0} is decidable.

Solution

This problem requires you to recognize that if C is a

context free language and R is a regular language, then C

R is context free. You have to show this, but it has been

done for you as the solution to problem 2.18. “On input : 1.

Construct CFG H st L(H) = 1* L(G). 2. Test whether L(H) =

, using the ECFG decider R from Theorem 4.8. 3. If R

accepts, reject; if R rejects, accept.”

MoreOver before proving this therom you need to know

about what is deciablility in Context Free Grammar

Are all decision problems decidable? Given a non-empty

alphabet : How many languages over are there? How

many Turing machines with alphabet are there? Choose

from finite, countable infinite, or uncountable.

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Let Sigma = {0,1}. Show that { | G is a CFG over {0,1} and 1* L{(G) 0} is decidable. Solution This problem requires you to recognize that if C is a context free language and R is a regular language, then C R is context free. You have to show this, but it has been done for you as the solution to pr ...
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