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103
Algebraic Algorithms for Sampling from Conditional Distributions
 Annals of Statistics
, 1995
"... We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so a ..."
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Cited by 192 (16 self)
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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
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Cited by 90 (17 self)
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Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
Reasoning with Concrete Domains
, 1999
"... Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importa ..."
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Cited by 54 (11 self)
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Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importance of this combined approach, especially for building realworld applications, is widely accepted. However, the complexity of reasoning with concrete domains has never been formally analyzed and efficient algorithms have not been developed. This paper closes the gap by providing a tight bound for the complexity of reasoning with concrete domains and presenting optimal algorithms. 1 Introduction Description logics are knowledge representation and reasoning formalisms dealing with conceptual knowledge on an abstract logical level. However, for a variety of applications, it is essential to integrate the abstract knowledge with knowledge of a more concrete nature. Examples of such "co...
Characteristicfree bounds for the Castelnuovo Mumford regularity
 Compos. Math
"... Abstract. In this paper we show how, given a complex of graded modules and knowing some partial CastelnuovoMumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity of the zero homology. We use this to prove that if ..."
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Cited by 28 (0 self)
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Abstract. In this paper we show how, given a complex of graded modules and knowing some partial CastelnuovoMumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity of the zero homology. We use this to prove that if dim TorR 1 (M, N) ≤ 1 then reg(M ⊗N) ≤ reg(M)+reg(N), generalizing results of Chandler, Conca and Herzog, and Sidman. Finally we give a description of the regularity of a module in terms of the postulation numbers of filter regular hyperplane restrictions. 1. introduction Let R = K[X1,..., Xn] be a polynomial ring over a field K, M a finitely generated graded Rmodule and let I ⊂ R be an ideal. Recently some work has been done to study when the CastelnuovoMumford regularity of Ir can be bounded by r times the regularity of I, and more generally when the regularity of IM can be bounded by the sum of the regularity of I and M. This is not always the case; see the papers of Sturmfels [St], and Conca, Herzog [CH] for counterexamples. On the
Linear Logic
, 1992
"... this paper we will restrict attention to propositional linear logic. The sequent calculus notation, due to Gentzen [10], uses roman letters for propositions, and greek letters for sequences of formulas. A sequent is composed of two sequences of formulas separated by a `, or turnstile symbol. One may ..."
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Cited by 24 (1 self)
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this paper we will restrict attention to propositional linear logic. The sequent calculus notation, due to Gentzen [10], uses roman letters for propositions, and greek letters for sequences of formulas. A sequent is composed of two sequences of formulas separated by a `, or turnstile symbol. One may read the sequent \Delta ` \Gamma as asserting that the multiplicative conjunction of the formulas in \Delta together imply the multiplicative disjunction of the formulas in \Gamma. A sequent calculus proof rule consists of a set of hypothesis sequents, displayed above a horizontal line, and a single conclusion sequent, displayed below the line, as below: Hypothesis1 Hypothesis2 Conclusion 4 Connections to Other Logics
Solving Degenerate Sparse Polynomial Systems Faster
 Journal of Symbolic Computation
, 1999
"... This paper is dedicated to my son, Victor Lorenzo. ..."
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Cited by 23 (3 self)
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This paper is dedicated to my son, Victor Lorenzo.