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Abit WI-2P Driver

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Abit WI-2P Driver

By Lemma 2.

De ne predicate e as follows: By 9 and 10the following properties hold. For every x, if x 2 L, then T x is at Abit WI-2P 2q jxj?

(PDF) The PL hierarchy collapses Mitsunori Ogihara -

It remains to show that h is in GapL. The constant 2 function is trivially in GapL and so, by Theorem 2. Since yx;i is logarithmic-space computable, by Theorem 2. This implies e 2 GapL. De ne G to be the nondeterministic Turing machine that, on input Abit WI-2P, behaves as follows: Step 1 G rst sets a one-bit memory c to 0.

Step Abit WI-2P G starts simulating N on x nondeterministically; that is, if N makes its ith nondeterministic move, then so does G Abit WI-2P guessing bit ui. When N makes its ith query yx;i, G does the following. If D rejects, then G ips bit c.

Step 3 When N enters the halting state, G does the following. Since G accepts if and only if the parity is 0, the number of accepting computation paths along w and u is the sum of all Y Y acc D Abit WI-2P i; wi rej D x; i; wi i62I i2I with I ranging over all subsets of f1;: Also, Abit WI-2P number of rejecting computation paths generated along w and u is the sum of all Y Y acc D x; i; wi rej D x; i; wi i62I i2I with I ranging over all subsets of f1;: Note for every i and wi, that acc D x; i; wi? Thus, the di erence between the above two sums is equal to jxj pY jxj pY acc D x; i; wi?

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This proves the theorem. Corollary 3.

ABIT - Workstation ( Socket 604 ) wi-2p

Once we obtain the closure prop- erty, it is easy to extend it to the closure property under logspace-uniform constant-depth, unbounded-fan-in circuit Abit WI-2P, in which arbitrary modulo q gates and threshold gates are allowed. We currently do not know the answer to the question.

Acknowledgment The author would like to thank Eric Allender for Abit WI-2P discussions and insightful com- ments. References [AO94] E. Allender and M.

Index of /

Abit WI-2P Relationships among PL, L, and the determinant. Bounded-width polynomial-size branching programs recognize ex- actly those languages in NC1. Journal of Computer and System Science, Borodin, S.


Cook, and N. Parallel computation for well-endowed rings and space-bounded probabilistic machines.

Information and Control, Beigel, N. Reingold, and D. PP is closed under intersection.

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A taxonomy of Abit WI-2P with fast parallel algorithms. Information and Computation, Fenner, L. Fortnow, and S. Gap-de nable counting classes.


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