# 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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