solutions3 - Solutions 3 Question 1 Show that cfw_P | P is...

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Solutions 3 Question 1 Show that { P | P is a position in the game where A has a winning strategy } is in PSPACE. A reminder of the definitions: a language is in AP if it is decided by an alternating Turing machine N (a non-deterministic TM whose states Q are divided into two parts Q and and Q or ) and all accepting computations use only polynomial time. An eventually accepting configuration (e.a.c.) of N on input x is defined as follows: all accepting leaves in the computation tree N ( x ) are e.a.c; a configuration with state in Q and is e.a.c. iff all its successor configurations are e.a.c; A configuration with state in Q or is e.a.c. iff at least one of its successor configurations is e.a.c. N accepts x iff the initial configuration of N ( x ) is e.a.c. Thus to answer the question we must describe a machine N that decides the language given in the question; let’s call it L . We do this by describing the computation tree N ( x ). Each vertex in the tree will correspond to a position in the game. The root corresponds to the position given in the input, and we define further vertices recursively: a vertex representing a position
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This note was uploaded on 01/29/2012 for the course ECE 345 taught by Professor Veneris during the Fall '10 term at University of Toronto- Toronto.

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solutions3 - Solutions 3 Question 1 Show that cfw_P | P is...

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