Thomas Thierauf

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Threshold machines are Turing machines whose acceptance is determined by what portion of the machine's computation paths are accepting paths. Probabilistic machines are Turing machines whose acceptance is determined by the probability weight of the machine's accepting computation paths. In 1975, Simon proved that for unbounded-error polynomial-time machines(More)
We show that MAEXP, the exponential time version of the Merlin-Arthur class, does not have polynomial size circuits. This significantly improves the previous known result due to Kannan since we furthermore show that our result does not relativize. This is the first separation result in complexity theory that does not relativize. As a corollary to our(More)
Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity. There is a significant gap between extant lower and upper bounds for planar graphs as well. We bridge the gap for this natural and important special case by presenting an upper bound that matches the known(More)
We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the veriier has access to an NP oracle. To obtain this, we use a(More)
We consider uniform subclasses of the nonuniform complexity classes de ned by Karp and Lipton via the notion of advice functions These subclasses are obtained by restricting the complexity of computing correct advice We also investigate the e ect of allowing advice functions of limited complexity to depend on the input rather than on the input s length(More)
Thecorrelation between two Boolean functions ofn inputs is defined as the number of times the functions agree minus the number of times they disagree, all divided by 2 n . In this paper we compute, in closed form, the correlation between any twosymmetric Boolean functions. As a consequence of our main result, we get that every symmetric Boolean function(More)
We show that the bipartite perfect matching problem is in quasi- <i>NC</i><sup>2</sup>. That is, it has uniform circuits of quasi-polynomial size&#xA0;<i>n</i><sup><i>O</i>(log<i>n</i>)</sup>, and <i>O</i>(log<sup>2</sup> <i>n</i>) depth. Previously, only an exponential upper bound was known on the size of such circuits with poly-logarithmic depth. We(More)
The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3-connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class AC 1. In this paper we improve the upper bound for planar 3-connected graphs to unambiguous logspace, in fact to UL∩coUL. As a consequence of our method we(More)
The perfect matching problem is known to be in P, in randomizedNC, and it is hard for NL. Whether the perfect matching problem is in NC is one of the most prominent open questions in complexity theory regarding parallel computations. Grigoriev and Karpinski [GK87] studied the perfect matching problem for bipartite graphs with polynomially bounded permanent.(More)