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Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b
#PCOMPLETE CONDITIONAL DISTRIBUTIONS
"... Abstract. We study conditional probability from the perspective of complexity theory of functions and operators in analysis, building on work by Ko (1983), Friedman (1984), and Kawamura and Cook (2010). For some random variable X in {0, 1} N whose distribution is continuous and polynomialtime compu ..."
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∈ A given f(X) ∈ B is shown to be #Pcomplete. On the other hand, all such functions computing conditional probabilities are in #P. 1.
A Theory Of Strict PCompleteness
 STACS 1992, in Lecture Notes in Computer Science 577
, 1992
"... . A serious limitation of the theory of Pcompleteness is that it fails to distinguish between those Pcomplete problems that do have polynomial speedup on parallel machines from those that don't. We introduce the notion of strict Pcompleteness and develop tools to prove precise limits on the ..."
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. A serious limitation of the theory of Pcompleteness is that it fails to distinguish between those Pcomplete problems that do have polynomial speedup on parallel machines from those that don't. We introduce the notion of strict Pcompleteness and develop tools to prove precise limits
Strict sequential Pcompleteness
 Proceedings of the 14th STACS, number 1200 in LNCS
, 1996
"... Abstract. In this paper we present a new notion of what it means for a problem in P to be inherently sequential. Informally, a problem L is strictly sequential Pcomplete if when the best known sequential algorithm for L has polynomial speedup by parallelization, this implies that all problems in P ..."
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Abstract. In this paper we present a new notion of what it means for a problem in P to be inherently sequential. Informally, a problem L is strictly sequential Pcomplete if when the best known sequential algorithm for L has polynomial speedup by parallelization, this implies that all problems in P
On #Pcompleteness of Some Counting Problems
"... We prove that the counting problems #1in3Sat, #NotAllEqual 3Sat and #3Colorability, whose decision counterparts have been the most frequently used in proving NPhardness of new decision problems, are #Pcomplete. On one hand, the explicit #Pcompleteness proof of #1in3Sat could be useful to p ..."
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to prove complexity results within unication theory. On the other hand, the fact that #3Colorability is #Pcomplete allows us to deduce immediately that the enumerative versions of a large class of NPcomplete problems are #Pcomplete. Moreover, our proofs shed some new light on the interest
Counting Eulerian Circuits is #PComplete
, 2004
"... Abstract We show that the problem of counting the number ofEulerian circuits in an undirected graph is complete for the class #P. The method employed is modp reductionfrom counting Eulerian orientations. 1 Introduction Every basic text in graph theory contains the storyof Euler and the K"o ..."
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Abstract We show that the problem of counting the number ofEulerian circuits in an undirected graph is complete for the class #P. The method employed is modp reductionfrom counting Eulerian orientations. 1 Introduction Every basic text in graph theory contains the storyof Euler and the K
BreadthDepth Search is Pcomplete
, 1994
"... The parallel complexity of a search strategy that combines attributes of both breadthfirst search and depthfirst search is studied. The search called breadthdepth search was defined by Horowitz and Sahni. The search technique has applications in branchandbound strategies. Kindervater and Lenstr ..."
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and Lenstra posed the complexity of this type of search strategy as an open problem. We resolve their question by showing that a natural decision problem based on breadthdepth search is Pcomplete. Specifically, we prove that if given a graph G = (V; E) either directed or undirected, a start vertex s 2 V
Counting Eulerian Circuits is #PComplete
"... We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P. The method employed is modp reduction from counting Eulerian orientations. ..."
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We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P. The method employed is modp reduction from counting Eulerian orientations.
Parallelizability of some Pcomplete problems ⋆
"... Abstract. In this paper, we consider parallelizability of some Pcomplete problems. First we propose a parameter which indicates parallelizability for a convex layers problem. We prove Pcompleteness of the problem and propose a cost optimal parallel algorithm, according to the parameter. Second we c ..."
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Abstract. In this paper, we consider parallelizability of some Pcomplete problems. First we propose a parameter which indicates parallelizability for a convex layers problem. We prove Pcompleteness of the problem and propose a cost optimal parallel algorithm, according to the parameter. Second we
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