The Effects of Adding Reachability Predicates in Propositional Separation Logic

Demri, Stéphane; Lozes, Étienne; Mansutti, Alessio

doi:10.1007/978-3-319-89366-2_26

Cited by 18 publications

(50 citation statements)

References 37 publications

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“…3) We establish that the satisfiability and entailment problem for full propositional separation logic with the singly-linked list-segment predicate is decidable in our semantics (in PSpace)-in stark contrast to the aforementioned undecidability result obtained by Demri et al [16] assuming the standard semantics.…”

Section: Why Should I Care?mentioning

confidence: 52%

“…In particular, this includes heaps with arbitrary dangling pointers into the list segment ls(x, nil). This power of introducing arbitrary dangling pointers is what is used by Demri et al for their undecidability proof of propositional separation logic with the singly-linked list-segment predicate [16].…”

Section: Introductionmentioning

confidence: 99%

“…This arbitrary splitting and adding of heaps makes reasoning about SL formulas difficult, and quickly renders separation logic undecidable when inductive predicates for data structures are considered. For example, Demri et al recently showed that adding only the singly-linked list-segment predicate to propositional separation logic (i.e., with * , − * and classical connectives ∧, ∨, ¬) leads to undecidability [16].…”

Section: Introductionmentioning

confidence: 99%

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Strong-Separation Logic

Pagel

Zuleger

2021

Programming Languages and Systems

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Most automated verifiers for separation logic are based on the symbolic-heap fragment, which disallows both the magic-wand operator and the application of classical Boolean operators to spatial formulas. This is not surprising, as support for the magic wand quickly leads to undecidability, especially when combined with inductive predicates for reasoning about data structures. To circumvent these undecidability results, we propose assigning a more restrictive semantics to the separating conjunction. We argue that the resulting logic, strong-separation logic, can be used for symbolic execution and abductive reasoning just like “standard” separation logic, while remaining decidable even in the presence of both the magic wand and the list-segment predicate—a combination of features that leads to undecidability for the standard semantics.

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Section: Why Should I Care?mentioning

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strong-Separation Logic

Pagel

Zuleger

2021

Programming Languages and Systems

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“…Once a framework provides a solid foundation for reasoning tasks, a natural step is to extend its expressiveness while keeping its complexity in check. Sometimes the additional capabilities do not change the complexity of the logic, as for example ( * ) extended with reachability predicates, whose satisfiability problem is still PSPACE-complete [20]. However, it often happens that the new features make the problem jump to higher complexity classes and, sometimes, reach MSO.…”

Section: Introductionmentioning

confidence: 99%

An Auxiliary Logic on Trees: on the Tower-Hardness of Logics Featuring Reachability and Submodel Reasoning

Mansutti

2020

Lecture Notes in Computer Science

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We describe a set of simple features that are sufficient in order to make the satisfiability problem of logics interpreted on trees TOWER-hard. We exhibit these features through an Auxiliary Logic on Trees (ALT), a modal logic that essentially deals with reachability of a fixed node inside a forest and features modalities from sabotage modal logic to reason on submodels. After showing that ALT admits a TOWER-complete satisfiability problem, we prove that this logic is captured by four other logics that were independently found to be TOWER-complete: twovariables separation logic, quantified computation tree logic, modal logic of heaps and modal separation logic. As a by-product of establishing these connections, we discover strict fragments of these logics that are still non-elementary.

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“…This fragment of the logic enjoys decidability in polynomial time [11] and is therefore highly suitable for use in large-scale analysers. However, in recent years, various authors have investigated the computational complexity of (and/or developed prototype analysers for) many other fragments employing various different assertion constructs, including user-defined inductive predicates [18,5,7,1,10], pointers with fractional permissions [22,13], arrays [6,19], separating implication (− − * ) [9,4], reachability predicates [14] and arithmetic [20,21].…”

Section: Introductionmentioning

confidence: 99%

On the Complexity of Pointer Arithmetic in Separation Logic

Brotherston

Kanovich

2018

Programming Languages and Systems

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We investigate the complexity consequences of adding pointer arithmetic to separation logic. Specifically, we study extensions of the points-to fragment of symbolic-heap separation logic with various forms of Presburger arithmetic constraints. Most significantly, we find that, even in the minimal case when we allow only conjunctions of simple "difference constraints" x ′ ≤ x ± k (where k is an integer), polynomial-time decidability is already impossible: satisfiability becomes NP-complete, while quantifier-free entailment becomes coNP-complete and quantified entailment becomes Π P 2 -complete (Π P 2 is the second class in the polynomial-time hierarchy) In fact we prove that the upper bound is the same, Π P 2 , even for the full pointer arithmetic but with a fixed pointer offset, where we allow any Boolean combinations of the elementary formulas (x ′ = x + k0), (x ′ ≤ x + k0), and (x ′ < x + k0), and, in addition to the points-to formulas, we allow spatial formulas of the arrays the length of which is ≤ k0 and lists which length is ≤ k0, etc, where k0 is a fixed integer. However, if we allow a significantly more expressive form of pointer arithmetic -namely arbitrary Boolean combinations of elementary formulas over arbitrary pointer sums -then the complexity increase is relatively modest for satisfiability and quantifier-free entailment: they are still NPcomplete and coNP-complete respectively, and the complexity appears to increase drastically for quantified entailments, which becomes Π EXP 1 complete.

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The Effects of Adding Reachability Predicates in Propositional Separation Logic

Cited by 18 publications

References 37 publications

Strong-Separation Logic

Strong-Separation Logic

An Auxiliary Logic on Trees: on the Tower-Hardness of Logics Featuring Reachability and Submodel Reasoning

On the Complexity of Pointer Arithmetic in Separation Logic

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