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Unformatted text preview: CS 181 — Winter 2008 Formal Languages and Automata Theory Problem Set #6 Solutions Problem 6.1. (10 points) Show that a language for which there exists an enumerator that enumer- ates the language in increasing lexicographical order is a decidable language. [For this, give a high level description of a Turing machine that halts on all inputs and accepts exactly the language.] Solution Let L be a language and E an enumerator that lists the words of L in increasing lexicographical order (i.e. by length, breaking ties lexicographically). We will show how build a Turing machine M that decides L . Given a word w , we can check to see if w ∈ L by comparing w with each of the words enumerated by E in order. If w ∈ L then eventually we’ll find a match. However, if w / ∈ L , then we may continue forever. Yet we can take advantage of the fact that E enumerates the words in increasing length. In particular, we can check w against the enumerated words until the length of the enumerated words becomes larger than that of w . If this is the case, then we know w will never appear in E ’s list and so must not be in L ....
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This homework help was uploaded on 04/02/2008 for the course COM SCI 181 taught by Professor Griebach during the Spring '08 term at UCLA.
- Spring '08