725-hw4-sp-06

# 725-hw4-sp-06 - and NotDEC TM are not Turing-recognizable...

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CSE 725 — Spring, 2006 Homework 4 Due: Wednesday, May 17 (start of class) 1. Prove that the set K = { M M Σ M * and M ( M ) halts} does not correspond to a property of languages. 2. Complete Case II of the proof of Rice's Theorem for decidable properties of languages. The situation is: Given: P is a decidable property of languages. Assume: P ≠∅ and P ALL -TMs and M i 0 P , where L ( M i 0 ) = . Show: HATLT TM m P . 3. Use Rice's Lemma 1 to show that E TM , FINITE TM , DEC TM
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Unformatted text preview: , and NotDEC TM are not Turing-recognizable, where E TM = { M L ( M ) = ∅ } , FINITE TM = { M L ( M ) is a finite set} , DEC TM = { M L ( M ) is Turing-decidable} , and NotDEC TM = { M L ( M ) is not Turing-decidable} . 4. Use Rice's Lemma 2 to show that ALL TM and INF TM are not Turing-recognizable, where ALL TM = { M L ( M ) = M * } and INF TM = { M L ( M ) is an infinite set} ....
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