Efficient Automated Reasoning About Sets and Multisets with Cardinality Constraints

Piskač, Ružica

doi:10.1007/978-3-030-51074-9_1

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…• SSL-REACHABILITY. This is the collection of problems used by Piskac et al (Piskac 2020) to evaluate their method based on a LIA* encoding of problems with multisets and cardinality constraints.…”

Section: Empirical Evaluationmentioning

confidence: 99%

“…In a further development, Piskac and Kuncak (Piskac and Kuncak 2008) give a decision procedure for multisets with cardinality constraints by using a similar method (i.e., encoding input formulas as quantifier-free PA formulas); more recently a more efficient method based on a LIA * encoding has been proposed (Piskac 2020;Levatich et al 2020). These algorithms have been implemented in the MUNCH (Piskac and Kuncak 2010) and ssl-reachability (Piskac 2020) tools which use existing solvers to solve the various problems derived from this approach, e.g., linear integer arithmetic.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Integrating Cardinality Constraints into Constraint Logic Programming with Sets

Cristiá¹,

Rossi²

2021

Preprint

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Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its elements are. The Constraint Logic Programming tool {log} provides a decision procedure for deciding the satisfiability of formulas involving very general forms of finite sets, without cardinality. In this paper we adapt and integrate a decision procedure for a theory of finite sets with cardinality into {log}. The proposed solver is proved to be a decision procedure for its formulas. Besides, the new CLP instance is implemented as part of the {log} tool. In turn, the implementation uses Howe and King's Prolog SAT solver and Prolog's CLP(Q) library, as an integer linear programming solver. The empirical evaluation of this implementation based on +250 real verification conditions shows that it can be useful in practice.

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Section: Empirical Evaluationmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Integrating Cardinality Constraints into Constraint Logic Programming with Sets

Cristiá¹,

Rossi²

2021

Preprint

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show abstract

“…Example 5.1: {log} has been tested against +250 verification conditions arising during the analysis of distributed algorithms [Pis20]. For instance, it can automatically discharge the following proof obligation.…”

Section: Dealing With Set Cardinalitiesmentioning

confidence: 99%

$\{log\}$: Set Formulas as Programs

Cristiá,

Rossi

2021

Preprint

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{log} is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But {log} is also a satisfiability solver for a theory of finite sets and finite binary relations. With {log} programmers can write abstract programs using all the power of set theory and binary relations. These programs are not very efficient but they are very close to specifications. Then, their correctness is more evident. Furthermore, {log} programs are also set formulas. Hence, programmers can use {log} again to automatically prove their programs verify non trivial properties. In this paper we show this development methodology by means of several examples.

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Succinct ordering and aggregation constraints in algebraic array theories

Raya,

Kunčak

2024

Journal of Logical and Algebraic Methods in Programming

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Efficient Automated Reasoning About Sets and Multisets with Cardinality Constraints

Cited by 4 publications

References 13 publications

Integrating Cardinality Constraints into Constraint Logic Programming with Sets

Integrating Cardinality Constraints into Constraint Logic Programming with Sets

$\{log\}$: Set Formulas as Programs

Succinct ordering and aggregation constraints in algebraic array theories

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