First-Order Transitive Closure Axiomatization via Iterative Invariant Injections

Ghazi, Aboubakr Achraf El; Taghdiri, Mana; Herda, Mihai

doi:10.1007/978-3-319-17524-9_11

Cited by 4 publications

(4 citation statements)

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“…For a finite scope, it is possible to expand the meaning of transitive closure as is done by Kodkod. El Ghazi et al [10] addresses this problem for unbounded scope by axiomatizing transitive closure in FOL, in an iterative manner.…”

Section: Related Workmentioning

confidence: 99%

Astra Version 1.0: Evaluating Translations from Alloy to SMT-LIB

Abbassi¹,

Day²,

Rayside³

2019

Preprint

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We present a variety of translation options for converting Alloy to SMT-LIB via Alloy's Kodkod interface. Our translations, which are implemented in a library that we call Astra, are based on converting the set and relational operations of Alloy into their equivalent in typed first-order logic (TFOL). We investigate and compare the performance of an SMT solver for many translation options. We compare using only one universal type to recovering Alloy type information from the Kodkod representation and using multiple types in TFOL. We compare a direct translation of the relations to predicates in TFOL to one where we recover functions from their relational form in Kodkod and represent these as functions in TFOL. We compare representations in TFOL with unbounded scopes to ones with bounded scopes, either pre or post quantifier expansion. Our results across all these dimensions provide directions for portfolio solvers, modelling improvements, and optimizing SMT solvers.

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Section: Related Workmentioning

confidence: 99%

Astra Version 1.0: Evaluating Translations from Alloy to SMT-LIB

Abbassi¹,

Day²,

Rayside³

2019

Preprint

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“…From this action, we should infer the relation (n, m) n ≤ m , as the reflexive-transitive closure of (n, n + 1) n ∈ Z . It is generally beyond the ability of SMT solvers to compute transitive closures, although some (limited) approaches have been proposed [14].…”

Section: Interference Reasoningmentioning

confidence: 99%

Caper

Dinsdale-Young

Pinto

Andersen

et al. 2017

Programming Languages and Systems

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Recent program logics based on separation logic emphasise a modular approach to proving functional correctness for fine-grained concurrent programs. However, these logics have no automation support. In this paper, we present Caper, a prototype tool for automated reasoning in such a logic. Caper is based on symbolic execution, integrating reasoning about interference on shared data and about ghost resources that are used to mediate this interference. This enables Caper to verify the functional correctness of fine-grained concurrent algorithms.

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“…We considered two sets of Alloy benchmarks; the first consists of examples from the Alloy distribution and from a formal methods course; the second were used by El Ghazi et al [33] to evaluate AlloyPE. AlloyPE is prototype tool that translates…”

Section: Experimental Evaluation On Alloy Modelsmentioning

confidence: 99%

“…Later, the same authors introduced more general methods [32,33] In this chapter, we present a theory-independent symmetry detection technique to detect partial symmetries for SMT formulas in polynomial time based on the semantic invariant of terms by permutation of variables, and also describe an algorithm to generate symmetry breaking constraints for symmetric variables of various types. The two algorithms were implemented in the SMT solver cvc4 and were evaluated on the SMT-LIB benchmarks, which shows some interesting results.…”

Section: Related Workmentioning

confidence: 99%

Satisfiability modulo relations

Meng¹

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First-Order Transitive Closure Axiomatization via Iterative Invariant Injections

Cited by 4 publications

References 15 publications

Astra Version 1.0: Evaluating Translations from Alloy to SMT-LIB

Astra Version 1.0: Evaluating Translations from Alloy to SMT-LIB

Caper

Satisfiability modulo relations

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