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The complexity of temporal constraint satisfaction problems
 J. ACM
"... A temporal constraint language is a set of relations that has a firstorder definition in (Q; <), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint langu ..."
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Cited by 18 (13 self)
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A temporal constraint language is a set of relations that has a firstorder definition in (Q; <), the dense linear order of the rational numbers. We present a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint languages, then the CSP can be solved in polynomial time; otherwise, the CSP is NPcomplete. Our proof combines modeltheoretic concepts with techniques from universal algebra, and also applies the socalled product Ramsey theorem, which we believe will useful in similar contexts of
Degree spectra of prime models
 J. Symbolic Logic
, 2004
"... 2.1 Notation from model theory................... 4 2.2 F ..."
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Cited by 8 (2 self)
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2.1 Notation from model theory................... 4 2.2 F
Semantic integration through invariants
 AI Mag
, 2005
"... Many tasks require correct and meaningful communication and integration among intelligent agents and information resources. A major barrier to such interoperability is semantic heterogeneity: different applications, databases, and agents may ascribe disparate meanings to the same terms or use distin ..."
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Cited by 7 (0 self)
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Many tasks require correct and meaningful communication and integration among intelligent agents and information resources. A major barrier to such interoperability is semantic heterogeneity: different applications, databases, and agents may ascribe disparate meanings to the same terms or use distinct terms to convey the same meaning. The development
A FAST ALGORITHM AND DATALOG INEXPRESSIBILITY FOR TEMPORAL REASONING
, 2009
"... We introduce a new tractable temporal constraint language, which strictly contains the OrdHorn language of Bürkert and Nebel and the class of AND/OR precedence constraints. The algorithm we present for this language decides whether a given set of constraints is consistent in time that is quadratic ..."
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Cited by 6 (5 self)
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We introduce a new tractable temporal constraint language, which strictly contains the OrdHorn language of Bürkert and Nebel and the class of AND/OR precedence constraints. The algorithm we present for this language decides whether a given set of constraints is consistent in time that is quadratic in the input size. We also prove that (unlike OrdHorn) the constraint satisfaction problem of this language cannot be solved by Datalog or by establishing local consistency.
New coins from old: Computing with unknown bias
 Combinatorica
"... Suppose that we are given a function f: (0, 1) → (0, 1) and, for some unknown p ∈ (0, 1), a sequence of independent tosses of a pcoin (i.e., a coin with probability p of “heads”). For which functions f is it possible to simulate an f(p)coin? This question was raised by S. Asmussen and J. Propp. A ..."
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Cited by 6 (2 self)
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Suppose that we are given a function f: (0, 1) → (0, 1) and, for some unknown p ∈ (0, 1), a sequence of independent tosses of a pcoin (i.e., a coin with probability p of “heads”). For which functions f is it possible to simulate an f(p)coin? This question was raised by S. Asmussen and J. Propp. A simple simulation scheme for the constant function f(p) ≡ 1/2 was described by von Neumann (1951); this scheme can be easily implemented using a finite automaton. We prove that in general, an f(p)coin can be simulated by a finite automaton for all p ∈ (0, 1), if and only if f is a rational function over Q. We also show that if an f(p)coin can be simulated by a pushdown automaton, then f is an algebraic function over Q; however, pushdown automata can simulate f(p)coins for certain nonrational functions such as f(p) = √ p. These results complement the work of Keane and O’Brien (1994), who determined the functions f for which an f(p)coin can be simulated when there are no computational restrictions on the simulation scheme. 1
Shlapentokh; Turing degrees of isomorphism types of algebraic objects
 Journal of the London Mathematical Society
"... ..."
Comparing classes of finite structures
 Algebra and Logic
"... In many branches of mathematics, there is work classifying a collection of objects, up to isomorphism or other important equivalence, in terms of nice invariants. In descriptive set theory, there is a body of work using a notion of ..."
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Cited by 5 (3 self)
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In many branches of mathematics, there is work classifying a collection of objects, up to isomorphism or other important equivalence, in terms of nice invariants. In descriptive set theory, there is a body of work using a notion of
Quantified equality constraints
 In Proceedings of LICS’07
, 2007
"... An equality template (also equality constraint language) is a relational structure with infinite universe whose relations can be defined by boolean combinations of equalities. We prove a complete complexity classification for quantified constraint satisfaction problems (QCSPs) over equality template ..."
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Cited by 5 (4 self)
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An equality template (also equality constraint language) is a relational structure with infinite universe whose relations can be defined by boolean combinations of equalities. We prove a complete complexity classification for quantified constraint satisfaction problems (QCSPs) over equality templates: these problems are in L (decidable in logarithmic space), NPcomplete, or PSPACEcomplete. To establish our classification theorem we combine methods from universal algebra with concepts from model theory. 1
AN ELEMENTARY AND CONSTRUCTIVE SOLUTION TO HILBERT’S 17TH PROBLEM FOR MATRICES
"... Abstract. We give a short and elementary proof of a theorem of Procesi, Schacher and (independently) Gondard, Ribenboim that generalizes a famous result of Artin. Let A be an n × n symmetric matrix with entries in the polynomial ring R[x1,..., xm]. The result is that if A is postive semidefinite for ..."
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Cited by 4 (1 self)
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Abstract. We give a short and elementary proof of a theorem of Procesi, Schacher and (independently) Gondard, Ribenboim that generalizes a famous result of Artin. Let A be an n × n symmetric matrix with entries in the polynomial ring R[x1,..., xm]. The result is that if A is postive semidefinite for all substitutions (x1,..., xm) ∈ Rm, then A can be expressed as a sum of squares of symmetric matrices with entries in R(x1,..., xm). Moreover, our proof is constructive and gives explicit representations modulo the scalar case. We shall give an elementary proof of the following theorem. Recall that a real matrix is positive semidefinite if it is symmetric with all nonnegative eigenvalues. Theorem 1. Let A be a symmetric matrix with entries in R[x1,..., xm]. If A is postive semidefinite for all substitutions (x1,..., xm) ∈ R m, then A can be expressed as a sum of squares of symmetric matrices with entries in R(x1,..., xm). This generalizes the following famous result of Artin on nonnegative polynomials; it is the starting point for a large body of work relating positivity and algebra. Theorem 2 (Artin). If f ∈ R[x1,..., xm] is nonnegative for all substitutions