Foundations for Decision Problems in Separation Logic with General Inductive Predicates

Antonopoulos, Timos; Gorogiannis, Nikos; Haase, Christoph; Kanovich, Max I.; Ouaknine, Joël

doi:10.1007/978-3-642-54830-7_27

Cited by 49 publications

(76 citation statements)

References 22 publications

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“…It was shown in [4] that the set of valid sequents is not recursively enumerable (and, therefore, validity is, in general, undecidable). However, it does turn out to be co-recursively enumerable.…”

Section: This Means That S |=mentioning

confidence: 99%

“…Indeed, there are now even tools capable of automatically generating the definitions of inductive predicates needed for analysis [11,25]. On the theoretical side, the satisfiability problem for our logic was recently shown decidable [10] and its entailment problem undecidable [4], although decidability results have been obtained for restricted classes of entailments [5,22]. Alongside these theoretical developments, there are automated tools geared towards the proof [13,17] and disproof [12] of entailments, as needed to support program verification.…”

Section: Introductionmentioning

confidence: 99%

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Model checking for symbolic-heap separation logic with inductive predicates

et al. 2016

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Copyright and moral rights to this thesis/research project are retained by the author and/or other copyright owners. The work is supplied on the understanding that any use for commercial gain is strictly forbidden. A copy may be downloaded for personal, non-commercial, research or study without prior permission and without charge. Any use of the thesis/research project for private study or research must be properly acknowledged with reference to the work's full bibliographic details.This thesis/research project may not be reproduced in any format or medium, or extensive quotations taken from it, or its content changed in any way, without first obtaining permission in writing from the copyright holder(s).If you believe that any material held in the repository infringes copyright law, please contact the Repository Team at Middlesex University via the following email address:eprints@mdx.ac.ukThe item will be removed from the repository while any claim is being investigated. AbstractWe investigate the model checking problem for symbolic-heap separation logic with user-defined inductive predicates, i.e., the problem of checking that a given stack-heap memory state satisfies a given formula in this language, as arises e.g. in software testing or runtime verification. First, we show that the problem is decidable; specifically, we present a bottom-up fixed point algorithm that decides the problem and runs in exponential time in the size of the problem instance.Second, we show that, while model checking for the full language is EXPTIME-complete, the problem becomes NP-complete or PTIME-solvable when we impose natural syntactic restrictions on the schemata defining the inductive predicates. We additionally present NP and PTIME algorithms for these restricted fragments.Finally, we report on the experimental performance of our procedures on a variety of specifications extracted from programs, exercising multiple combinations of syntactic restrictions.

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Section: This Means That S |=mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Model checking for symbolic-heap separation logic with inductive predicates

et al. 2016

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“…show invalid) an entailment A B, we need to exhibit a countermodel (s, h) such that s, h |= Φ A but s, h |= Φ B. Unfortunately, this is not straightforward, since the entailment problem for our fragment of separation logic is undecidable [3].…”

Section: An Algorithm For Entailment Disproofmentioning

confidence: 99%

“…This fragment is much more expressive than the simple linked-list fragment, but is also computationally much harder. In particular, entailment in this fragment is undecidable [3], although satisfiability is decidable [10] and entailment is decidable when predicates are restricted to have bounded treewidth [19].…”

Section: Introductionmentioning

confidence: 99%

Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

Brotherston

Gorogiannis

2015

Lecture Notes in Computer Science

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Abstract. We give a procedure for establishing the invalidity of logical entailments in the symbolic heap fragment of separation logic with user-defined inductive predicates, as used in program verification. This disproof procedure attempts to infer the existence of a countermodel to an entailment by comparing computable model summaries, a.k.a. bases (modified from earlier work), of its antecedent and consequent. Our method is sound and terminating, but necessarily incomplete. Experiments with the implementation of our disproof procedure indicate that it can correctly identify a substantial proportion of the invalid entailments that arise in practice, at reasonably low time cost. Accordingly, it can be used, e.g., to improve the output of theorem provers by returning "no" answers in addition to "yes" and "unknown" answers to entailment questions, and to speed up proof search or automated theory exploration by filtering out invalid entailments.

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“…In principle, definitions could be partially ordered by entailment (cf. [12]) but for our language this is known to be undecidable [1]. Instead, we manually classify solutions into three categories.…”

Section: Implementation and Evaluationmentioning

confidence: 99%

Cyclic Abduction of Inductively Defined Safety and Termination Preconditions

Brotherston

Gorogiannis

2014

Static Analysis

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Abstract. We introduce cyclic abduction: a new method for automatically inferring safety and termination preconditions of heap-manipulating while programs, expressed as inductive definitions in separation logic. Cyclic abduction essentially works by searching for a cyclic proof of the desired property, abducing definitional clauses of the precondition as necessary in order to advance the proof search process. We provide an implementation, Caber, of our cyclic abduction method, based on a suite of heuristically guided tactics. It is often able to automatically infer preconditions describing lists, trees, cyclic and composite structures which, in other tools, previously had to be supplied by hand.

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Foundations for Decision Problems in Separation Logic with General Inductive Predicates

Cited by 49 publications

References 22 publications

Model checking for symbolic-heap separation logic with inductive predicates

Model checking for symbolic-heap separation logic with inductive predicates

Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

Cyclic Abduction of Inductively Defined Safety and Termination Preconditions

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