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Generating NonRedundant Association Rules
, 2000
"... The traditional association rule mining framework produces many redundant rules. The extent of redundancy is a lot larger than previously suspected. We present a new framework for associations based on the novel concept of closed frequent itemsets. The number of nonredundant rules produced by the n ..."
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Cited by 237 (11 self)
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The traditional association rule mining framework produces many redundant rules. The extent of redundancy is a lot larger than previously suspected. We present a new framework for associations based on the novel concept of closed frequent itemsets. The number of nonredundant rules produced
Full Abstraction for PCF
 INFORMATION AND COMPUTATION
, 1996
"... An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable i ..."
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Cited by 254 (16 self)
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An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies, and show that it satisfies some remarkable properties, such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an orderextensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntaxindependent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model, and prove a Universality Theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence.
On the Complexity of Unification and Disunification in Commutative Idempotent Semigroups
 In Principles and Practice of Constraint Programming  CP97, Third International Conference
, 1997
"... . We analyze the computational complexity of elementary unification and disunification problems for the equational theory ACI of commutative idempotent semigroups. From earlier work, it was known that the decision problem for elementary ACIunification is solvable in polynomial time. We show that th ..."
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Cited by 1 (0 self)
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that this problem is inherently sequential by establishing that it is complete for polynomial time (Pcomplete) via logarithmicspace reductions. We also investigate the decision problem and the counting problem for elementary ACImatching and observe that the former is solvable in logarithmic space, but the latter
Solving Systems of Polynomial Equations
 AMERICAN MATHEMATICAL SOCIETY, CBMS REGIONAL CONFERENCES SERIES, NO 97
, 2002
"... One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, ..."
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Cited by 221 (14 self)
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One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, machine learning, control theory, and numerous other areas. The set of solutions to a system of polynomial equations is an algebraic variety, the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting recent developments in symbolic algebra and numerical software for geometric calculations have revolutionized the field, making formerly inaccessible problems tractable, and providing fertile ground for experimentation and conjecture. The first half of this book furnishes an introduction and represents a snapshot of the state of the art regarding systems of polynomial equations. Afficionados of the wellknown text books by Cox, Little, and O’Shea will find familiar themes in the first five chapters: polynomials in one variable, Gröbner
IDEMPOTENT ULTRAFILTERS AND POLYNOMIAL RECURRENCE
, 711
"... Abstract. We give a new proof of a polynomial recurrence result due to Bergelson, Furstenberg, and McCutcheon, using idempotent ultrafilters instead of IPlimits. ..."
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Cited by 1 (0 self)
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Abstract. We give a new proof of a polynomial recurrence result due to Bergelson, Furstenberg, and McCutcheon, using idempotent ultrafilters instead of IPlimits.
Satisfiability modulo recursive programs
 In Static Analysis Symposium (SAS
, 2011
"... Abstract. We present a semidecision procedure for checking satisfiability of expressive correctness properties of recursive firstorder functional programs. In our approach, both properties and programs are expressed in the same language, a subset of Scala. We implemented our procedure and integrat ..."
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Cited by 31 (15 self)
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and integrated it with the Z3 SMT solver and the Scala compiler. Our procedure is sound for counterexamples and for proofs of terminating functions. It is terminating and thus complete for many important classes of specifications, including all satisfiable formulas and all formulas where recursive functions
SemiringBased Constraint Satisfaction and Optimization
 JOURNAL OF THE ACM
, 1997
"... We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be asso ..."
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Cited by 207 (26 self)
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to be associated with each tuple of values of the variable domain, and the two semiring operations (1 and 3) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain
SOS Rule Formats for Idempotent Terms and Idempotent Unary Operators ✩
"... A unary operator f is idempotent if the equation f(x) = f(f(x)) holds. On the other end, an element a of an algebra is said to be an idempotent for a binary operator ⊙ if a = a ⊙ a. This paper presents a rule format for Structural Operational Semantics that guarantees that a unary operator be idemp ..."
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be idempotent modulo bisimilarity. The proposed rule format relies on a companion one ensuring that certain terms are idempotent with respect to some binary operator. This study also offers a variety of examples showing the applicability of both formats.
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