A2 - Department of Computer Science COMPSCI 350 Assignment...

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Unformatted text preview: Department of Computer Science COMPSCI 350 Assignment 2 Due: May 15 1. Show that ALL DFA = {h B i | B } is DFA and L ( B ) = Σ * } is decidable. [10 marks] Solution: The following Turing machine decides ALL DFA : M = “on input h B i where B is a DFA: 1. Let C be the DFA obtained by interchanging accepting and rejecting states of B . 2. Run TM T from Thm. 4.4 on input h C i to see whether L ( C ) = ∅ . 3. If so ACCEPT, otherwise REJECT.” 2. Show that the subset problem for DFA is decidable. Namely, {h B,C i | B,C are DFA and L ( B ) ⊆ L ( C ) } is decidable. [10 marks] Solution: (Sketch) This is similar to Theorem 4.5 that EQ DFA is decidable. From input h B,C i a Turing machine constructs a DFA D recognizing L ( B ) ∩ L ( C ). Then it accepts if L ( D ) is empty, otherwise it rejects. 3. (Sipser 4.28) Let A be a Turing recognizable language consisting of descriptions h M i of Turing machines M that are all deciders....
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A2 - Department of Computer Science COMPSCI 350 Assignment...

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