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Bound Propagation for Arithmetic Reasoning in Vampire

by Ioan Dragan, Konstantin Korovin, Andrei Voronkov
"... Abstract—This paper describes an implementation and exper-imental evaluation of a recently introduced bound propagation method for solving systems of linear inequalities over the reals and rationals. The implementation is part of the first-order theorem prover Vampire. The input problems are systems ..."
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Abstract—This paper describes an implementation and exper-imental evaluation of a recently introduced bound propagation method for solving systems of linear inequalities over the reals and rationals. The implementation is part of the first-order theorem prover Vampire. The input problems

Interval propagation to reason about sets: definition and implementation of a practical language

by Carmen Gervet - CONSTRAINTS , 1997
"... Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes difficu ..."
Abstract - Cited by 119 (8 self) - Add to MetaCart
optimization problems by applying a cost function to the quantifiable, i.e., arithmetic, terms which are associated to set terms. The constraint solving in Conjunto is based on local consistency techniques using interval reasoning which are extended to handle set constraints. The main contribution

Coil sensitivity encoding for fast MRI. In:

by Klaas P Pruessmann , Markus Weiger , Markus B Scheidegger , Peter Boesiger - Proceedings of the ISMRM 6th Annual Meeting, , 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
Abstract - Cited by 193 (3 self) - Add to MetaCart
imaging techniques, MRI stands out by a rarely stated peculiarity: the size of the details resolved with MRI is much smaller than the wavelength of the radiation involved. The reason for this surprising ability is that the origin of a resonance signal is not determined by optical means such as focusing

Combinatorics in Bounded Arithmetics

by Kerry Ojakian , 2004
"... A basic aim of logic is to consider what axioms are used in proving various theorems of mathematics. This thesis will be concerned with such issues applied to a particular area of mathematics: combinatorics. We will consider two widely known groups of proof methods in combinatorics, namely, probabil ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
, probabilistic methods and methods using linear algebra. We will consider certain applications of such methods, both of which are significant to Ramsey theory. The systems we choose to work in are various theories of bounded arithmetic. For the probabilistic method, the key point is that we use the weak

Residual belief propagation: Informed scheduling for asynchronous message passing

by Gal Elidan - in Proceedings of the Twenty-second Conference on Uncertainty in AI (UAI , 2006
"... Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard, real-life inference tasks. While it is widely recognized that ..."
Abstract - Cited by 110 (3 self) - Add to MetaCart
that the scheduling of messages in these algorithms may have significant consequences, this issue remains largely unexplored. In this work, we address the question of how to schedule messages for asynchronous propagation so that a fixed point is reached faster and more often. We first show that any reasonable

Lower Bounds for Propositional Proofs and Independence Results in Bounded Arithmetic

by Alexander A. Razborov - Proceedings of the 23rd ICALP, Lecture Notes in Computer Science , 1996
"... . We begin with a highly informal discussion of the role played by Bounded Arithmetic and propositional proof systems in the reasoning about the world of feasible computations. Then we survey some known lower bounds on the complexity of proofs in various propositional proof systems, paying special a ..."
Abstract - Cited by 26 (10 self) - Add to MetaCart
. We begin with a highly informal discussion of the role played by Bounded Arithmetic and propositional proof systems in the reasoning about the world of feasible computations. Then we survey some known lower bounds on the complexity of proofs in various propositional proof systems, paying special

Efficient solving of large non-linear arithmetic constraint systems with complex boolean structure,”

by Martin Fränzle , Christian Herde , Stefan Ratschan , Tobias Schubert - Journal on Satisfiability, Boolean Modeling, and Computation, , 2007
"... Abstract In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with interval-based arithmetic constraint solving. Our approach deviates subst ..."
Abstract - Cited by 90 (12 self) - Add to MetaCart
Abstract In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with interval-based arithmetic constraint solving. Our approach deviates

Bounded Arithmetic and Formalizing Probabilistic Proofs

by Dai Tri Man Lê , 2014
"... The first theme of this thesis investigates the complexity class CC and its associated bounded-arithmetic theory. Subramanian defined CC as the class of problems log-space reducible to the comparator circuit value problem (Ccv). Using the Cook-Nguyen method we define the two-sorted theory VCC whose ..."
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that the universal polynomial-time theory VPV augmented with the surjective weak pigeonhole principle sWPHP(LFP) for all VPV functions is the ‘right’ theory for randomized polynomial-time reasoning in bounded arithmetic. Motivated from the fact that no one had used Jeˇrábek’s framework for feasible reasoning about

CONSTRAINT REASONING BASED ON INTERVAL ARITHMETIC 1

by unknown authors
"... Current numerical constraint propagation systems accept as input only problems represented by exact numerical values and correspondingly produce only crisp solutions as output. In order to remove this limitation we have designed and implemented a generalized constraint propagation scheme based on in ..."
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Current numerical constraint propagation systems accept as input only problems represented by exact numerical values and correspondingly produce only crisp solutions as output. In order to remove this limitation we have designed and implemented a generalized constraint propagation scheme based

Variety Reasoning for Multiset Constraint Propagation

by Y. C. Law, J. H. M. Lee, M. H. C. Woo , 2009
"... Set variables in constraint satisfaction problems (CSPs) are typically propagated by enforcing set bounds consistency together with cardinality reasoning, which uses some inference rules involving the cardinality of a set variable to produce more prunings than set bounds propagation alone. Multiset ..."
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Set variables in constraint satisfaction problems (CSPs) are typically propagated by enforcing set bounds consistency together with cardinality reasoning, which uses some inference rules involving the cardinality of a set variable to produce more prunings than set bounds propagation alone. Multiset
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