A Machine Program for Theorem Proving

Davis, Martin; Logemann, George; Loveland, Donald W.

doi:10.1007/978-3-642-81952-0_16

Cited by 516 publications

(727 citation statements)

References 3 publications

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“…Initially, each variable receives its whole domain as an interval valuation. Akin to DPLL-based SAT solving [3,4], the three main ingredients of the solver are deduction, decision, and conflict resolution. However, constraints cannot only be satisfied or unsatisfied for all valuations from the interval box, but also contain a mixture of points satisfying or violating a constraint.…”

Section: Flow Invariantsmentioning

confidence: 99%

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

et al. 2012

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Aiming at automatic verification and analysis techniques for hybrid discrete-continuous systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art interval solver for ODEs, and with bracketing systems, which exploit monotonicity properties allowing to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply the combined iSAT-ODE solver to the analysis of a variety of non-linear hybrid systems by solving predicative encodings of reachability properties and of an inductive stability argument, and evaluate the impact of the different enclosure methods, decision heuristics and their combination. Our experiments include classic benchmarks A preliminary version of this paper appeared in [6]. from the literature, as well as a newly-designed conveyor belt system that combines hybrid behavior of parallel components, a slip-stick friction model with non-linear dynamics and flow invariants and several dimensions of parameterization. In the paper, we also present and evaluate an extension of VNODE-LP tailored to its use as a deduction mechanism within iSAT-ODE, to allow fast re-evaluations of enclosures over arbitrary subranges of the analyzed time span.

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Section: Flow Invariantsmentioning

confidence: 99%

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

et al. 2012

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“…We will see that myopic SAT algorithms are (for the most part) priority algorithms or small width pBT algorithms. The most popular methods for solving SAT are DPLL algorithms-a family of backtracking algorithms whose complexity has been characterized in terms of resolution proof complexity (see for example Cook & Mitchell 1997;Davis et al 1962;Davis & Putnam 1960;Gu et al 1997). The pBT model encompasses DPLL in many situations where access to the input is limited to some extent.…”

Section: Brief History Of Related Workmentioning

confidence: 99%

Toward a Model for Backtracking and Dynamic Programming

et al. 2011

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We propose a model called priority branching trees (pBT ) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and Satisfiability.

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“…Although testing orientability of matroids is known to be NP-complete [35], experimentally our method achieves satisfactory results. The motivation for this approach is the fact that although SAT is also NP-complete, practical heuristics [11,12] and fast implementations [14] are known. Using our method we determine orientability of matroids with r = 3, n ≤ 12 and r = 4, n ≤ 9.…”

Section: From Matroids To Oriented Matroidsmentioning

confidence: 99%

Matroid Enumeration for Incidence Geometry

Matsumoto

Moriyama

Imai

et al. 2011

Discrete Comput Geom

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Matroids are combinatorial abstractions for point configurations and hyperplane arrangements, which are fundamental objects in discrete geometry. Matroids merely encode incidence information of geometric configurations such as collinearity or coplanarity, but they are still enough to describe many problems in discrete geometry, which are called incidence problems. We investigate two kinds of incidence problem, the points-lines-planes conjecture and the so-called Sylvester-Gallai type problems derived from the Sylvester-Gallai theorem, by developing a new algorithm for the enumeration of non-isomorphic matroids. We confirm the conjectures of Welsh-Seymour on ≤11 points in R 3 and that of Motzkin on ≤12 lines in R 2 , extending previous results. With respect to matroids, this algorithm succeeds to enumerate a complete list of the isomorph-free rank 4 matroids on 10 elements. When geometric configurations corresponding to specific matroids are of interest in some incidence problems, they should be analyzed on oriented matroids. Using an encoding of oriented matroid axioms as a boolean satisfiability (SAT) problem, we also enumerate oriented matroids from the matroids of rank 3 on n ≤ 12 elements and rank 4 on n ≤ 9 elements. We further list several new minimal non-orientable matroids.

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A Machine Program for Theorem Proving

Cited by 516 publications

References 3 publications

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

Improving the SAT modulo ODE approach to hybrid systems analysis by combining different enclosure methods

Toward a Model for Backtracking and Dynamic Programming

Matroid Enumeration for Incidence Geometry

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