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We introduce a new class of functions, called span functions which count the different output values that occur at the leaves of the computation tree associated with a nondeterministic polynomial time Turing machine transducer. This function class has natural complete problems; it is placed between Valiant's function classes # P and =~ NP, and contains both… (More)

We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomial-time hierarchy PH to ZPP(NP) under the assumption that NP has polynomial-size circuits. This improves on the well-known result of Karp, Lipton, and Sipser [KL80] stating a collapse… (More)

We show that the graph isomorphism problem is low for PP and for C = P, i.e., it does not provide a PP or C = P computation with any additional power when used as an oracle. Furthermore, we show that graph isomorphism belongs to the class LWPP (see Fenner, Fortnow, Kurtz 12]). A similar result holds for the (apparently more diicult) problem Group… (More)

We investigate the computational power of the new counting class ModP which generalizes the classes Mod p P, p prime. We show that ModP is polynomial-time truth-table equivalent in power to #P and that ModP is contained in the class AmpMP. As a consequence, the classes PP, ModP and AmpMP are all Turing equivalent, and thus AmpMP and ModP are not low for MP… (More)

We show that, for k constant, k-tree isomorphism can be decided in logarithmic space by giving a logspace canonical labeling algorithm. The algorithm computes a unique tree decomposition, uses colors to fully encode the structure of the original graph in the decomposition tree and invokes Lindell's tree canonization algorithm. As a consequence, the… (More)

It is shown that the assumption of NP having polynomial-size circuits implies (apart from a collapse of the polynomial-time hierarchy as shown by Karp and Lip-ton) that the classes AM and MA of Babai's Arthur-Merlin hierarchy coincide. This means that also a certain inner collapse of the remaining classes of the polynomial-time hierarchy occurs. It is well… (More)

We show that the class of sets having polynomial size circuits , P=poly, has EXP NP-measure zero under each of the following two assumptions: EXP NP 6 = ZPP p 2 (which holds if the polynomial time hierarchy does not collapse to ZPP p 2), or NP is not small (does not have EXP-measure zero).

We present a logspace algorithm that constructs a canonical intersection model for a given proper circular-arc graph, where canonical means that models of isomorphic graphs are equal. This implies that the recognition and the isomorphism problems for this class of graphs are solvable in logspace. For a broader class of concave-round graphs, that still… (More)