048_Computability_theory-part_4

048_Computability_theory-part_4 - Selected exercises with...

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Unformatted text preview: Selected exercises with solutions on Computability theory in the field of the Theory of computation Part 4 Amir Semmo Extracted from former homeworks in the course "Theory of computation II", Summer term 2008, University of Potsdam October 6, 2008 Exercise Sheet 4 Exercise 1 Let A = {h R,S i | R and S are regular expressions and L ( R ) ⊆ L ( S ) } . Show that A is decidable. We know that every regular expression RE can be converted in an equivalent NFA N , where L ( N ) = L ( RE ) . Furthermore every NFA can be converted into an equiv- alent DFA. We construct a Turin Machine M, which makes use of the just named conversions and decides the language A : TM M = "On input h R,S i : 1. Construct the equivalent NFA's B and C for the regular expressions R and S . 2. Construct the equivalent DFA's D and E for the NFA's B and C . 3. Construct a new DFA F , which accepts the language L ( F ) = L ( D ) ∩ L ( B ) . 4. Simulate the decider for the language E DFA ( note: L ( E DFA = {h A i | A is a DFA and L ( A ) = ∅} ). We accept when E DFA accepts, and we...
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This note was uploaded on 02/22/2010 for the course CS 881 taught by Professor H.f. during the Spring '10 term at Shahid Beheshti University.

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048_Computability_theory-part_4 - Selected exercises with...

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