Tractable and Intractable Entailment Problems in Separation Logic with Inductively Defined Predicates
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916856561926144 |
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| author | Echenim, Mnacho Peltier, Nicolas |
| author_facet | Echenim, Mnacho Peltier, Nicolas |
| contents | We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on the inductive rules that define the semantics of the predicates. We focus on so-called P-rules, which are similar to (but simpler than) the PCE rules introduced by Iosif et al. in 2013. In particular, for a specific fragment where predicates are defined by so-called loc-deterministic inductive rules, we devise a sound and complete cyclic proof procedure running in polynomial time. Several complexity lower bounds are provided, showing that any relaxing of the provided conditions makes the problem intractable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_08419 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tractable and Intractable Entailment Problems in Separation Logic with Inductively Defined Predicates Echenim, Mnacho Peltier, Nicolas Logic in Computer Science 68T27 I.2.3; F.4.1 We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on the inductive rules that define the semantics of the predicates. We focus on so-called P-rules, which are similar to (but simpler than) the PCE rules introduced by Iosif et al. in 2013. In particular, for a specific fragment where predicates are defined by so-called loc-deterministic inductive rules, we devise a sound and complete cyclic proof procedure running in polynomial time. Several complexity lower bounds are provided, showing that any relaxing of the provided conditions makes the problem intractable. |
| title | Tractable and Intractable Entailment Problems in Separation Logic with Inductively Defined Predicates |
| topic | Logic in Computer Science 68T27 I.2.3; F.4.1 |
| url | https://arxiv.org/abs/2305.08419 |