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solutions3

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

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