Conflict Resolution

Korovin, Konstantin; Tsiskaridze, Nestan; Воронков, Андрей

doi:10.1007/978-3-642-04244-7_41

Cited by 30 publications

(27 citation statements)

References 6 publications

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“…To explain the rationale behind this strategy we refer to the notion of 'almost' nonredundant constraints, defined in [1]. For readers' convenience we recall this notion here.…”

Section: Strategies For Selecting Conflictsmentioning

confidence: 99%

“…In this paper we present an evaluation of our conflict resolution method [1] for checking solvability of systems of linear inequalities.…”

Section: Introductionmentioning

confidence: 99%

“…The process continues until either the assignment is refined into a solution, or a trivially unsatisfiable inequality is derived, showing unstaisfiability of the initial system of inequalities. In [1] the conflict resolution method is shown to be sound, complete and terminating.…”

Section: Introductionmentioning

confidence: 99%

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Implementing Conflict Resolution

Korovin

Tsiskaridze

Воронков

2012

Perspectives of Systems Informatics

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Abstract. The conflict resolution method, introduced by the authors in [1] is a new method for solving systems of linear inequalities over the rational and real numbers. This paper investigates various heuristics for optimisation of the method and presents experimental evaluation. The method and heuristics are evaluated against various benchmarks and compared to other methods, such as the FourierMotzkin elimination method and the simplex method.

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“…To explain the rationale behind this strategy we refer to the notion of 'almost' nonredundant constraints, defined in [1]. For readers' convenience we recall this notion here.…”

Section: Strategies For Selecting Conflictsmentioning

confidence: 99%

“…In this paper we present an evaluation of our conflict resolution method [1] for checking solvability of systems of linear inequalities.…”

Section: Introductionmentioning

confidence: 99%

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Implementing Conflict Resolution

Korovin

Tsiskaridze

Воронков

2012

Perspectives of Systems Informatics

Self Cite

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“…Conflict-driven Tsatisfiability procedures [45,39,22,37,38,32] are not compatible in general with DPLL(T ), and therefore one cannot get a conflict-driven T -decision procedure by plugging a conflict-driven T -satisfiability procedure into DPLL(T ). A reason of incompatibility is that DPLL(T ) does not allow the creation of new atoms, whereas a conflict-driven T -satisfiability procedure may need to generate a clause that contains new atoms in order to explain a conflict [27].…”

Section: The Mcsat Frameworkmentioning

confidence: 99%

“…In other words, the T -solver implements a conflict-driven T -satisfiability procedure. Such procedures exist for linear real arithmetic [45,39,22], linear integer arithmetic [57,55,37], non-linear arithmetic [38], and floating-point binary arithmetic [32].…”

Section: Conflict-driven Theory Reasoningmentioning

confidence: 99%

On Conflict-Driven Reasoning

Bonacina

Kalpa Publications in Computing

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Automated formal methods and automated reasoning are interconnected, as formal methods generate reasoning problems and incorporate reasoning techniques. For example, formal methods tools employ reasoning engines to find solutions of sets of constraints, or proofs of conjectures. From a reasoning perspective, the expressivity of the logical language is often directly proportional to the difficulty of the problem. In propositional logic, Conflict-Driven Clause Learning (CDCL) is one of the key features of state-of-the-art satisfiability solvers. The idea is to restrict inferences to those needed to explain conflicts, and use conflicts to prune a backtracking search. A current research direction in automated reasoning is to generalize this notion of conflict-driven satisfiability to a paradigm of conflict-driven reasoning in first-order theories for satisfiability modulo theories and assignments, and even in full first-order logic for generic automated theorem proving. While this is a promising and exciting lead, it also poses formidable challenges.

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Decomposing Farkas Interpolants

Blicha

Hyvärinen

Kofroň

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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Modern verification commonly models software with Boolean logic and a system of linear inequalities over reals and overapproximates the reachable states of the model with Craig interpolation to obtain, for example, candidates for inductive invariants. Interpolants for the linear system can be efficiently constructed from a Simplex refutation by applying the Farkas' lemma. However, Farkas interpolants do not always suit the verification task and in the worst case they may even be the cause of divergence of the verification algorithm. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants obtained by identifying and separating independent components from the interpolant structure using methods from linear algebra. We integrate our approach to the model checker Sally and show experimentally that a portfolio of decomposed interpolants results in immediate convergence on instances where state-of-the-art approaches diverge. Being based on the efficient Simplex method, the approach is very competitive also outside these diverging cases.

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Conflict Resolution

Cited by 30 publications

References 6 publications

Implementing Conflict Resolution

Implementing Conflict Resolution

On Conflict-Driven Reasoning

Decomposing Farkas Interpolants

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