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hwsol4.1

hwsol4.1 - Lofgren Musbach CSci 5403 Homework 4 Problem 1...

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Lofgren, Musbach CSci 5403— Homework 4 Problem 1 Suppose L PPSPACE . Then there exists a polynomial p : N N and a p ( n )-space PTM M that runs for exactly 2 p ( n ) steps on every input (it counts its steps to ensure this), has a unique accepting configuration a (it clears its tape before accepting), and is such that x L ⇐⇒ Pr[ M ( x )] 1 / 2. We will construct an algorithm that decides L in polynomial space, proving that L PSPACE . By δ ( x, b ), we mean the configuration that comes after configuration x with random bit b . By [ δ ( u, b ) = v ], we mean the Iverson bracket: 1 if δ ( u, b ) = v , and 0 otherwise. Let C be the set of configurations of M , so | C | = θ (2 p ( n ) ). We define a recursive function Count-Paths ( u, v, i ) which counts the number of computation paths from u to v of length 2 i : Count-Paths ( u, v, i ) = ( [ δ ( u, 0) = v ] + [ δ ( u,
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