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hw3A2009

# hw3A2009 - T such that L T = L i 2 Let T 1 T 2 T 3 … T n...

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CS 181 Homework 3 Context-free grammars, Turing machines, and inductive Turing machines Due Thursday, August 13, 2009 1. For each of the following languages L 1 = { a p ; p is a prime number }, L 2 = { a p ; p is a prime number, m is a fixed number and m p 0 }, L 3 = { a m b 2m c 3 m ; m 0 }, L 4 = { a m b 2 c 3 m ; m 0 }, find if it is: a) a regular language; b) a context-free language; c) a recursively enumerable language. In case (a) for the language L i , build a finite automaton A such that L( A ) = L i . In case (b), build a PDA D and a formal grammar G such that L( D ) = L(G) = L i . In case (c), build a TM
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Unformatted text preview: T such that L( T ) = L i . 2. Let T 1 , T 2 , T 3 , … , T n , … be a constructive enumeration of all Turing machines with alphabet {1, 0} and one linear tape. For each of the following sets X 1 = { p ; p is a prime number }, X 2 = { px ; p is a fixed prime number and x is a number of a Turing machine T x that halts given the input x }, X 3 = { x ; x is a number of a Turing machine T x that does not halt given the input x }, find if it is: a) decidable/recursive; b) recursively enumerable; c) inductively decidable....
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