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October 11 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing October 11, 2005
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October 11, 2005 Agenda Last week Prove equivalence of deterministic and  nondeterministic Turing machines Today Enumerators Definition of algorithm Another class of languages Decidable
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October 11, 2005 Announcements Quiz tomorrow High-level description of TM Trace through a TM’s operation Tape notation & configuration notation High-level description of equivalences Homework due next Tuesday (10/18) 4.4, 4.6, 4.7, 4.12, 4.19 Old text 4.4, 4.7, 4.8, 4.11, 4.19
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October 11, 2005 Enumerators Instead of reading an input and processing it,  enumerators start with an empty tape and print  out strings in  Σ * M Printer 1 1 2 1 3 ~ ~ ~ aaba bbcc aaaaabb
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October 11, 2005 Machine equivalence Theorem:   A language is Turing-recognizable if and  only of some enumerator enumerates it. Proof technique:   Construction in each direction
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October 11, 2005 TM accept enumerator language TM = “On input w: Run enumerator E.  Every time E prints a string,  compare it to w. If w appears in the output,  accept .”
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October 11, 2005 Enumerator accepts TM language • Let s 1 , s 2 , s 3 , … be all the strings in  Σ * E = “Ignore the input.
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