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The Dichotomy Theorem for evolution bifamilies
 J. Diff. Eq
"... We prove that the operator G, the closure of the firstorder differential operator −d/dt + D(t) on L2(R, X), is Fredholm if and only if the not wellposed equation u′(t) = D(t)u(t), t ∈ R, has exponential dichotomies on R+ and R − and the ranges of the dichotomy projections form a Fredholm pair; mo ..."
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Cited by 8 (5 self)
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We prove that the operator G, the closure of the firstorder differential operator −d/dt + D(t) on L2(R, X), is Fredholm if and only if the not wellposed equation u′(t) = D(t)u(t), t ∈ R, has exponential dichotomies on R+ and R − and the ranges of the dichotomy projections form a Fredholm pair
Toward a Dichotomy Theorem for Polynomial Evaluation
, 2009
"... A dichotomy theorem for counting problems due to Creignou and Hermann states that or any finite set S of logical relations, the counting problem #SAT(S) is either in FP, or #Pcomplete. In the present paper we study polynomial evaluation from this dichotomic point of view. We show that the “hard” ca ..."
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Cited by 5 (0 self)
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A dichotomy theorem for counting problems due to Creignou and Hermann states that or any finite set S of logical relations, the counting problem #SAT(S) is either in FP, or #Pcomplete. In the present paper we study polynomial evaluation from this dichotomic point of view. We show that the “hard
Dichotomy theorems for alternationbounded quantified Boolean formulas
, 2004
"... Abstract. In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems, showed that all these problems are either in P or NPcomplete, and gave a simple criterion to determine which of the two ca ..."
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Cited by 10 (1 self)
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Abstract. In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems, showed that all these problems are either in P or NPcomplete, and gave a simple criterion to determine which of the two
A Dichotomy Theorem for Learning Quantified Boolean Formulas
, 1997
"... We consider the following classes of quantified boolean formulas. Fix a finite set of basic boolean functions. Take conjunctions of these basic functions applied to variables and constants in arbitrary way. Finally quantify existentially or universally some of the variables. We prove the following d ..."
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Cited by 1 (1 self)
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dichotomy theorem: For any set of basic boolean functions, the resulting set of formulas is either polynomially learnable from equivalence queries alone or else it is not PACpredictable even with membership queries under cryptographic assumptions. Furthermore we identify precisely which sets of basic
Graph Homomorphisms with Complex Values: A Dichotomy Theorem
"... Graph homomorphism problem has been studied intensively. Given an m × m symmetric matrix A, the graph homomorphism function is defined as ZA(G) = Aξ(u),ξ(v), ξ:V →[m] (u,v)∈E where G = (V, E) is any undirected graph. The function ZA(G) can encode many interesting graph properties, including counting ..."
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Cited by 31 (14 self)
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Graph homomorphism problem has been studied intensively. Given an m × m symmetric matrix A, the graph homomorphism function is defined as ZA(G) = Aξ(u),ξ(v), ξ:V →[m] (u,v)∈E where G = (V, E) is any undirected graph. The function ZA(G) can encode many interesting graph properties, including counting vertex covers and kcolorings. We study the computational complexity of ZA(G) for arbitrary complex valued symmetric matrices A. Building on work by Dyer and Greenhill [6], Bulatov and Grohe [2], and especially the recent beautiful work by Goldberg,
On Kakutani's Dichotomy Theorem for Innite Products of not Necessarily Independent Functions
"... (1.1) Background. The background for the present communication is Kakutani's famous dichotomy theorem [10], viz.: if ( n; F n) is a sequence of measurable spaces and Pn and Qn are probability measures ..."
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(1.1) Background. The background for the present communication is Kakutani's famous dichotomy theorem [10], viz.: if ( n; F n) is a sequence of measurable spaces and Pn and Qn are probability measures
A Decidable Dichotomy Theorem on Directed Graph Homomorphisms with Nonnegative Weights
, 2010
"... The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this paper, we prove a decidable complexity dichotomy theorem for ..."
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Cited by 12 (8 self)
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The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this paper, we prove a decidable complexity dichotomy theorem
A note on Gowers' Dichotomy Theorem
 Conv. Geom. Anal
, 1998
"... Abstract. We present a direct proof, slightly different from the original, for an important special case of Gowers ’ general dichotomy result: If X is an arbitrary infinite dimensional Banach space, either X has a subspace with unconditional basis, or X contains a hereditarily indecomposable subspac ..."
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Cited by 3 (0 self)
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Abstract. We present a direct proof, slightly different from the original, for an important special case of Gowers ’ general dichotomy result: If X is an arbitrary infinite dimensional Banach space, either X has a subspace with unconditional basis, or X contains a hereditarily indecomposable
Results 1  10
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19,350