048_Computability_theory-part_4 - Selected exercises with...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 4

048_Computability_theory-part_4 - Selected exercises with...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online