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2001-Automata_and_Formal_Languages-scanned-solutions -...

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Salutione comprehemive exam Automata aad Formal Languages October 31, 2001 1. Dmw a nondetministie jinite automaton without &-moues (~cceptkg the language (ab)* + e. 3. Consider the following pmblern: Given descriptions of two &ring machines M and N over a given alphabet, is there a Btring accepted by both M and N? Is this problem decidable? No. By Rice's theorem it is undecidable whether a given Turing machine M accepts a non- empty language- That problem can be reduced to the problem above, by taking N to be a fixed Turing machine that accepts every string over the given alphabet. It follows that also the problem above is undecidable. Is it mursiue enumemble? Yes. Given descriptions of M and N, enumerate all pairs (w, n) with w a word over the given alphibet and n a natural number. For each such pair (ul,n) run both M snd N on w for n steps. In case both accept, return "Yesn.
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4. A clique of sise k in an undided gmph G is a subgmph math k nodes, wherein every two nodes are connected an edge.
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