MUP: a minimal unsatisfiability prover

Huang, Jing

doi:10.1109/aspdac.2005.1466202

Cited by 7 publications

(5 citation statements)

References 27 publications

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“…The UC extraction for LTL has also been the subject of several studies (Awad et al, 2011;Goré et al, 2013;Narizzano et al, 2018;Schuppan, 2016). Goré et al (2013) present a BDD based approach that leverages a method to determine minimal UCs for SAT (Huang, 2005) to find minimal UCs in LTL. In the work of Awad et al (2011), UCs are extracted by leveraging a tableau-based solver to obtain an initial subset of unsatisfiable LTL formulas and then applying a deletion-based minimisation to the subset.…”

Section: Related Workmentioning

confidence: 99%

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Computing Unsatisfiable Cores for LTLf Specifications

Roveri,

Di Ciccio,

Di Francescomarino

et al. 2024

jair

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Linear-time temporal logic on finite traces (LTLf) is rapidly becoming a de-facto standard to produce specifications in many application domains (including planning, business process management, run-time monitoring, and reactive synthesis). Several studies have challenged the satisfiability problem thus far. In this paper, we focus instead on unsatisfiable LTLf specifications, with the objective of extracting the subset of formulae that cause inconsistencies within them, i.e., the unsatisfiable cores. We provide four algorithms to this end, which leverage the adaptation of a range of state-of-the-art algorithms to LTLf satisfiability checking. We implement those algorithms extending the respective implementations and carry out an experimental evaluation on a set of reference benchmarks, restricting to the unsatisfiable specifications. The results put in evidence that the different algorithms and tools exhibit complementary features determining their efficiency and efficacy. Indeed, our findings suggest exploring different strategies and algorithmic solutions for the extraction of unsatisfiable cores from LTLf specifications, thus confirming the challenging and multi-faceted nature of this problem.

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Section: Related Workmentioning

confidence: 99%

“…Finally, we remark that works on propositional UC extraction (e.g., Goldberg and Novikov 2003;Huang 2005; Marques-Silva and Janota 2014) could be used to improve the quality of the computed cores. We leave this investigation for future developments.…”

Section: Related Workmentioning

confidence: 99%

Computing Unsatisfiable Cores for LTLf Specifications

Roveri,

Di Ciccio,

Di Francescomarino

et al. 2024

jair

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“…The naïve approach to MUC extraction, Dershowitz et al (2006), successively removes constraints and solves the problem again; if the problem is still infeasible after a constraint has been removed that constraint does not belong to a MUC. There exist more efficient approaches; the MUC (Huang 2005) algorithm based on efficient manipulation of Binary Decision Trees guarantees the extraction of a minimal Unsat Core. Nadel (2010) presents an algorithm based on the resolution graph (Kroening and Strichman 2016) for MUC extraction.…”

Section: The Minimal Unsat Corementioning

confidence: 99%

Conflict-free electric vehicle routing problem: an improved compositional algorithm

Roselli,

Fabian,

Åkesson

2023

Discrete Event Dyn Syst

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The Conflict-Free Electric Vehicle Routing Problem (CF-EVRP) is a combinatorial optimization problem of designing routes for vehicles to execute tasks such that a cost function, typically the number of vehicles or the total travelled distance, is minimized. The CF-EVRP involves constraints such as time windows on the tasks’ execution, limited operating range of the vehicles, and limited capacity on the number of vehicles that a road segment can simultaneously accommodate. In previous work, the compositional algorithm ComSat was introduced to solve the CF-EVRP by breaking it down into sub-problems and iteratively solve them to build an overall solution. Though ComSat showed good performance in general, some problem instances took significant time to solve due to the high number of iterations required to find solutions for two sub-problems, namely the Routing Problem, and the Paths Changing Problem. This paper addresses the bottlenecks of ComSat and presents new formulations for both sub-problems in order to reduce the number of iterations required to find feasible solutions to the CF-EVRP. Experiments on sets of benchmark instances show the effectiveness of the presented improvements.

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“…The closest related work can be found in the literature on generating or enumerating MUSs (Lynce & Silva, 2004;Bacchus & Katsirelos, 2016Liffiton, Previti, Malik, & Marques-Silva, 2016). Various techniques are used to find MUSs, including manipulation of resolution proofs produced by SAT solvers (Goldberg & Novikov, 2003;Gershman et al, 2008;Dershowitz et al, 2006), incremental solving to enable/disable clauses and branchand-bound search (Oh et al, 2004), BDD-manipulation methods (Huang, 2005). Some methods rely on seed-shrink algorithms (Bendík & Černá, 2020a(Bendík & Černá, , 2020b which repeatedly start from unsatisfiable seed (an unsatisfiable core) and shrink the seed to a MUS.…”

Section: Related Workmentioning

confidence: 99%

Efficiently Explaining CSPs with Unsatisfiable Subset Optimization

Gamba,

Bogaerts,

Guns

2023

jair

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We build on a recently proposed method for stepwise explaining the solutions to Constraint Satisfaction Problems (CSPs) in a human understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified by a cost function. Explanation generation algorithms rely on extracting Minimal Unsatisfiable Subsets (MUSs) of a derived unsatisfiable formula, exploiting a one-to-one correspondence between so-called non-redundant explanations and MUSs. However, MUS extraction algorithms do not guarantee subset minimality or optimality with respect to a given cost function. Therefore, we build on these formal foundations and address the main points of improvement, namely how to generate explanations efficiently that are provably optimal (with respect to the given cost metric). To this end, we developed (1) a hitting set-based algorithm for finding the optimal constrained unsatisfiable subsets; (2) a method for reusing relevant information across multiple algorithm calls; and (3) methods for exploiting domain-specific information to speed up the generation of explanation sequences. We have experimentally validated our algorithms on a large number of CSP problems. We found that our algorithms outperform the MUS approach in terms of explanation quality and computational time (on average up to 56 % faster than a standard MUS approach).

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MUP: a minimal unsatisfiability prover

Cited by 7 publications

References 27 publications

Computing Unsatisfiable Cores for LTLf Specifications

Computing Unsatisfiable Cores for LTLf Specifications

Conflict-free electric vehicle routing problem: an improved compositional algorithm

Efficiently Explaining CSPs with Unsatisfiable Subset Optimization

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