Theory-Specific Reasoning about Loops with Arrays using Vampire

Chen, Yuting; Kovács, Laura; Robillard, Simon

doi:10.29007/qk21

“…There is a substantial body of work on automated quantified invariant generation for arrays using first-order theorem provers [KV13,CKR16,KV09,McM08]. These include extensions to saturation-based theorem proving to analyze specific kinds of predicates, and an extension to paramodulation-based theorem proving to produce universally quantified interpolants.…”

Section: Related Workmentioning

confidence: 99%

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

Mann¹,

Irfan²,

Griggio³

et al. 2022

Logical Methods in Computer Science

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We develop a framework for model checking infinite-state systems by automatically augmenting them with auxiliary variables, enabling quantifier-free induction proofs for systems that would otherwise require quantified invariants. We combine this mechanism with a counterexample-guided abstraction refinement scheme for the theory of arrays. Our framework can thus, in many cases, reduce inductive reasoning with quantifiers and arrays to quantifier-free and array-free reasoning. We evaluate the approach on a wide set of benchmarks from the literature. The results show that our implementation often outperforms state-of-the-art tools, demonstrating its practical potential.

show abstract

“…There is a substantial body of work on automated quantified invariant generation for arrays using first-order theorem provers [42,16,41,51]. These include extensions to saturation-based theorem proving to analyze specific kinds of predicates, and an extension to paramodulation-based theorem proving to produce universally quantified interpolants.…”

Section: Related Workmentioning

confidence: 99%

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

Mann

¹

,

Irfan

²

,

Griggio

³

et al. 2021

Tools and Algorithms for the Construction and Analysis of Systems

View full text Add to dashboard Cite

We develop a framework for model checking infinite-state systems by automatically augmenting them with auxiliary variables, enabling quantifier-free induction proofs for systems that would otherwise require quantified invariants. We combine this mechanism with a counterexample-guided abstraction refinement scheme for the theory of arrays. Our framework can thus, in many cases, reduce inductive reasoning with quantifiers and arrays to quantifier-free and array-free reasoning. We evaluate the approach on a wide set of benchmarks from the literature. The results show that our implementation often outperforms state-of-the-art tools, demonstrating its practical potential.

show abstract

“…There is a substantial body of work on automated quantified invariant generation for arrays using first-order theorem provers [42,16,41,51]. These include extensions to saturation-based theorem proving to analyze specific kinds of predicates, and an extension to paramodulation-based theorem proving to produce universally quantified interpolants.…”

Section: Related Workmentioning

confidence: 99%

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

Mann¹

2021

Preprint

View full text Add to dashboard Cite

We develop a framework for model checking infinite-state systems by automatically augmenting them with auxiliary variables, enabling quantifier-free induction proofs for systems that would otherwise require quantified invariants. We combine this mechanism with a counterexample-guided abstraction refinement scheme for the theory of arrays. Our framework can thus, in many cases, reduce inductive reasoning with quantifiers and arrays to quantifier-free and array-free reasoning. We evaluate the approach on a wide set of benchmarks from the literature. The results show that our implementation often outperforms state-of-the-art tools, demonstrating its practical potential.

show abstract

Theory-Specific Reasoning about Loops with Arrays using Vampire

Cited by 6 publications

References 10 publications

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

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