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149,105
Efficient LoopCheck for Backward Proof Search in Some NonClassical Propositional Logics
, 1996
"... . We consider the modal logics KT and S4, the tense logic K t , and the fragment IPC (^;!) of intuitionistic logic. For these logics backward proof search in the standard sequent or tableau calculi does not terminate in general. In terms of the respective Kripke semantics, there are several kinds of ..."
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Cited by 39 (1 self)
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. We consider the modal logics KT and S4, the tense logic K t , and the fragment IPC (^;!) of intuitionistic logic. For these logics backward proof search in the standard sequent or tableau calculi does not terminate in general. In terms of the respective Kripke semantics, there are several kinds
The Foundation of a Generic Theorem Prover
 Journal of Automated Reasoning
, 1989
"... Isabelle [28, 30] is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a metalogic (or `logical framework') in which the objectlogics are formalized. Isabell ..."
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Cited by 471 (49 self)
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. Isabelle is now based on higherorder logic  a precise and wellunderstood foundation. Examples illustrate use of this metalogic to formalize logics and proofs. Axioms for firstorder logic are shown sound and complete. Backwards proof is formalized by metareasoning about objectlevel entailment
Logic Programming with Focusing Proofs in Linear Logic
 Journal of Logic and Computation
, 1992
"... The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is C ..."
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erent ..."
Abstract

Cited by 580 (6 self)
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#erential or di#erence equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between di#erent classes of orthogonal polynomials listed in the Askeyscheme. In chapter
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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be derived as specific instances of the sumproduct algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform algorithms.
Least angle regression
 Ann. Statist
"... The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to s ..."
Abstract

Cited by 1308 (43 self)
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The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope
Automatic verification of finitestate concurrent systems using temporal logic specifications
 ACM Transactions on Programming Languages and Systems
, 1986
"... We give an efficient procedure for verifying that a finitestate concurrent system meets a specification expressed in a (propositional, branchingtime) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent ..."
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Cited by 1384 (62 self)
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system. We also show how this approach can be adapted to handle fairness. We argue that our technique can provide a practical alternative to manual proof construction or use of a mechanical theorem prover for verifying many finitestate concurrent systems. Experimental results show that state machines
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
The Valuation of Options for Alternative Stochastic Processes
 Journal of Financial Economics
, 1976
"... This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have nol been used in previous models. The technique is applied lo these processes to find explicit option valuation formulas, ..."
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Cited by 661 (4 self)
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This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have nol been used in previous models. The technique is applied lo these processes to find explicit option valuation formulas, and solutions to some previously unsolved problems involving the pricing ofsecurities with payouts and potential bankruptcy. 1.
Mining Sequential Patterns
, 1995
"... We are given a large database of customer transactions, where each transaction consists of customerid, transaction time, and the items bought in the transaction. We introduce the problem of mining sequential patterns over such databases. We present three algorithms to solve this problem, and empiri ..."
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Cited by 1534 (7 self)
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We are given a large database of customer transactions, where each transaction consists of customerid, transaction time, and the items bought in the transaction. We introduce the problem of mining sequential patterns over such databases. We present three algorithms to solve this problem, and empirically evaluate their performance using synthetic data. Two of the proposed algorithms, AprioriSome and AprioriAll, have comparable performance, albeit AprioriSome performs a little better when the minimum number of customers that must support a sequential pattern is low. Scaleup experiments show that both AprioriSome and AprioriAll scale linearly with the number of customer transactions. They also have excellent scaleup properties with respect to the number of transactions per customer and the number of items in a transaction.
Results 1  10
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149,105