On the Almighty Wand

Brochenin, Rémi; Demri, Stéphane; Lozes, Étienne

doi:10.1007/978-3-540-87531-4_24

Cited by 40 publications

(92 citation statements)

References 26 publications

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“…Decidability results related to first-order separation logic are discussed in [8,6]. A fragment of separation logic for which it is decidable to check validity of entailments was introduced in [2].…”

Section: Related Workmentioning

confidence: 99%

Satisfiability modulo abstraction for separation logic with linked lists

Thakur

Breck

Reps

2014

Proceedings of the 2014 International SPIN Symposium on Model Checking of Software

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Abstract. Separation logic is an expressive logic for reasoning about heap structures in programs. This paper presents a semi-decision procedure for deciding unsatisfiability of formulas in a fragment of separation logic that includes predicates describing points-to assertions (x → y), acyclic-list-segment assertions(ls(x, y)), logical-and, logical-or, separating conjunction, and septraction (the DeMorgan-dual of separating implication). The fragment that we consider allows negation at leaves, and includes formulas that lie outside other separation-logic fragments considered in the literature.The semi-decision procedure is designed using concepts from abstract interpretation. The procedure uses an abstract domain of shape graphs to represent a set of heap structures, and computes an abstraction that over-approximates the set of satisfying models of a given formula. If the over-approximation is empty, then the formula is unsatisfiable. We have implemented the method, and evaluated it on a set of formulas taken from the literature. The implementation is able to establish the unsatisfiability of formulas that cannot be handled by other existing approaches.

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Section: Related Workmentioning

confidence: 99%

Satisfiability modulo abstraction for separation logic with linked lists

Thakur

Breck

Reps

2014

Proceedings of the 2014 International SPIN Symposium on Model Checking of Software

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“…The semantics of the non-obvious connectives is given below. In [1], the syntactic fragment SL( * ) is considered, in which the conjunction operation, * , is present but its adjoint the magic wand, − * , is absent. They show that this logic is decidable by a translation to MSO.…”

Section: Separation Logicmentioning

confidence: 99%

“…To be precise, we show that there is a property of unlabelled, directed forests that is expressible in MSO but not in GL. Since, on forests, one can replace quantification over sets of edges with quantification overs sets of vertices, this yields the stronger result that GL does not even contain MS 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Brochenin et al [1] consider the expressive power of SL( * ), which is separation logic with a separating conjunction ( * ) but without the magic wand (− * ) and conjecture that it is properly contained in MSO. Since SL is essentially the same as GL over structures known as memory heaps, and since the forests we use to separate GL from MSO can be coded as such heaps, a direct consequence of our proof is a positive resolution of this conjecture.…”

Section: Introductionmentioning

confidence: 99%

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Separating Graph Logic from MSO

Antonopoulos

Dawar

2009

Foundations of Software Science and Computational Structures

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Abstract. Graph logic (GL) is a spatial logic for querying graphs introduced by Cardelli et al. It has been observed that in terms of expressive power, this logic is a fragment of Monadic Second Order Logic (MSO), with quantification over sets of edges. We show that the containment is proper by exhibiting a property that is not GL definable but is definable in MSO, even in the absence of quantification over labels. Moreover, this holds when the graphs are restricted to be forests and thus strengthens in several ways a result of Marcinkowski. As a consequence we also obtain that Separation Logic, with a separating conjunction but without the magic wand, is strictly weaker than MSO over memory heaps, settling an open question of Brochenin et al.

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“…The model-checking, satisfiability, and validity problems for SL are pspace-complete. Decidable fragments of first-order SL can be found in [25,34,35].…”

Section: Lemma 12 (Small Memory State Property)mentioning

confidence: 99%

Reasoning About Sequences of Memory States

Brochenin

Demri

Lozes

Logical Foundations of Computer Science

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Motivated by the verification of programs with pointer variables, we introduce a temporal logic LTL mem whose underlying assertion language is the quantifier-free fragment of separation logic and the temporal logic on the top of it is the standard linear-time temporal logic LTL. We analyze the complexity of various model-checking and satisfiability problems for LTL mem , considering various fragments of separation logic (including pointer arithmetic), various classes of models (with or without constant heap), and the influence of fixing the initial memory state. We provide a complete picture based on these criteria. Our main decidability result is pspace-completeness of the satisfiability problems on the record fragment and on a classical fragment allowing pointer arithmetic. Σ 0 1 -completeness or Σ 1 1 -completeness results are established for various problems by reducing standard problems for Minsky machines, and underline the tightness of our decidability results.

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On the Almighty Wand

Cited by 40 publications

References 26 publications

Satisfiability modulo abstraction for separation logic with linked lists

Satisfiability modulo abstraction for separation logic with linked lists

Separating Graph Logic from MSO

Reasoning About Sequences of Memory States

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