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hw5-1

# hw5-1 - CSE 105 Automata and Computability Theory Winter...

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CSE 105: Automata and Computability Theory Winter 2011 Homework #5 Due: Tuesday, March 1st, 2011 Problem 1 Let COMPL DFA be the language h A, B i A and B are DFAs over the same alphabet Σ and L ( A ) = L ( B ) . (Notice the complementation bar over L ( B ) above!) Show that COMPL DFA is decid- able. Problem 2 We say that a string over the alphabet Σ = { 0 , 1 } is sorted if any 0s in it occur before any 1s. (For example, 111 is sorted, whereas 00110 is not.) We consider the empty string to be sorted. Let MESSY DFA be the language n h A i A is a DFA over the alphabet Σ = { 0 , 1 } and no string in L ( A ) is sorted o . Show that MESSY DFA is decidable. Hint: Think about intersecting two regular languages. Problem 3 (Sipser 4.22) A
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