W. Hesse, E. Allender, and D. A. M. Barrington. Uniform constant-depth threshold circuits for division and iterated multiplication. Journal of Computer and System Sciences, 65:695--716, 2002. Home/Search Document Details and Download
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Dynamic Computational Complexity - Hesse (2003) (Correct)
....which the formula #(x) is true. In the resulting formula, i is free and x is bound. Problems that are in FO(COUNT) include finding the sum of n n bit integers, finding the product of two n bit integers, finding the integer quotient of two n bit integers, and finding the product of n n bit integers [19]. This extra power can be used to create a fully dynamic algorithm for transitive closure. In other words, Theorem 5.1 DynREACH is in DynFO(COUNT) The proof of this theorem is the main content of this chapter. The class DynFO(COUNT) is defined from the static class FO(COUNT) by the standard ....
....intermediate values in the algorithm can be computed by TC circuits. The circuits will be simple to construct, and they will be composed in simple ways to compute the final results from the inputs. The most complex circuits used will be TC circuits raising an n bit number to the power n [19, 38]. Since the computation effected by each of these circuits can be described by a formula in FO(COUNT) the combined computation can be described by a combined formula in FO(COUNT) and therefore can be performed by a TC circuit. The formula for updating the a s,t upon inserting an edge ....
Hesse, Allender, and Barrington. Uniform constant-depth threshold circuits for division and iterated multiplication. JCSS: Journal of Computer and System Sciences 65 (2002).
Arithmetic Complexity, Kleene Closure, and Formal Power.. - Allender, Arvind, Mahajan (2003) Self-citation (Allender) (Correct)
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W. Hesse, E. Allender, and D. A. M. Barrington. Uniform constant-depth threshold circuits for division and iterated multiplication. Journal of Computer and System Sciences, 65:695--716, 2002.
Derandomization and Distinguishing Complexity - Allender, Koucky, Ronneburger.. (2003) Self-citation (Allender) (Correct)
....protocol is very easy to compute; it sends random sequences to each prover and receives from the provers sequences of polynomials on which it performs (in parallel) some consistency checks. The consistency checks involve field operations, which are computable by DLOGTIME uniform TC circuits [14]. All the queries to the provers are made in one round (and hence are nonadaptive) Since by assumption, ###### # NC that every language in NEXP is also in ##### . Now we prove the implication (# # #) We largely follow [15] where it is shown that if NEXP # P poly, then NEXP search can be ....
W. Hesse, E. Allender, and D. Barrington. Uniform constant-depth threshold circuits for division and iterated multiplication. Journal of Computer and System Sciences, 65:695--716, 2002.
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