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# ps3 - CSE105 Automata and Computability Theory Winter 2012...

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Unformatted text preview: CSE105: Automata and Computability Theory Winter 2012 Problem Set #3 Due: Monday, February 27th, 2012 Problem 1 A string x is a substring of a string y if there are some (possibly empty) strings u and v such that y = uxv . For example, 000 is a substring of 010001, but not of 00100; 101 is a substring of 101; and the empty string is a substring of 111. As before, x R denotes the symbol-by-symbol reverse of a string x . a. Show that the following language is context-free but not regular: L a = x R # y x,y ∈ { , 1 } * and x is a substring of y . b. Show that the following language is not context-free: L b = x # y x,y ∈ { , 1 } * and x is a substring of y . As examples, note that 01#0011 is in L b and 10#0011 is in L a , but not vice versa. Problem 2 The input to a Turing machine is always a string, but we will want to use Turing machines to reason not just about strings but about objects such as graphs, automata, grammars, and even other Turing machines. To do this, we will encode each...
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ps3 - CSE105 Automata and Computability Theory Winter 2012...

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