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Chapter 0: Q18P (page 1)
Let is a regular expression with exponentiation and }. Show that .
The above problem is solved by using i.e., the problem of any -complete cannot be in .
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Consider the undirected graph where, the set of nodes, is
and, the set of edges, is Draw the graphG. What are the degrees of each node? Indicate a path from node 3 to node 4 on your drawing ofG.
Let . Show that AMBIGCFG is undecidable. (Hint: Use a reduction from PCP. Given an instance
of the Post Correspondence Problem, construct a CFG Gwith the rules
where a1,...,ak are new terminal symbols. Prove that this reduction works.)
In the fixed-point version of the recursion theorem (Theorem 6.8), let the transformation t be a function that interchanges the states and in Turing machine descriptions. Give an example of a fixed point for t.
Show that the function K(x) is not a computable function.
Consider the language B=L(G), where Gis the grammar given in
Exercise 2.13. The pumping lemma for context-free languages, Theorem 2.34,
states the existence of a pumping length p for B . What is the minimum value
of p that works in the pumping lemma? Justify your answer.
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