C. Damm, M. Holzer, and P. Rossmanith. Expressing uniformity via oracles. Theory of Computing Systems, 30:355--366, 1997.  Home/Search   Document Details and Download   Summary   Related Articles

....families C = C n ) are equivalent: 1. LDC 2 DTIME(logn) UD uniformity) 2. LDC 2 ATIME(log n) 3. LEC 2 DTIME(logn) UE uniformity) 4. LDC 2 ATIME(log n) UE uniformity) 5. The description of C n is deterministically computable out of 1 n in logarithmic space (UBC uniformity) b)[20] For k 1, NC k is equal to the class of languages recognized by bounded fan circuits of polynomial size and depth O(log k n) such that LEC 2 NC k . c) For k 2, NC k is equal to the class of languages recognized by bounded fan circuits of polynomial size and depth O(log k n) such that ....

....implies (a) given in the above proof, we would only get that L belongs to AC k uniform NC k where AC k uniform means that the extended connection language of the circuit family is in AC k . However, the construction of (a) implies (b) together with the constructions of Damm et al. [20], give the converse. Hence, we have: Corollary 8 L 2 AC k uniform NC k if and only if L can be recognized by a simple CRCW PRAM A in time O(log k n) such that A has data independent control, read, and write structures. The last result shows how essential the complexity assumptions of the ....

C. Damm, M. Holzer, and P. Rossmanith. Expressing uniformity via oracles. Theory of Computing Systems, 30:355--366, 1997.

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