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The Complexity of Prenex Separation Logic with One Selector

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Mnacho Echenim, Radu Iosif, Nicolas Peltier

Logic in Computer Science · Submitted 10 Apr 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Second, we show that this entails the decidability of the finite and infinite satisfiability problem for the class of prenex formulas of $\seplogk{1}$, by reduction to the first-order theory of one unary function symbol and unary predicate symbols.

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arXiv ID1804.03556 (version 2)
Pith IDQZPALHVI, Pith's permanent record of this paper and its review
CitationMnacho Echenim, Nicolas Peltier, Radu Iosif. "The Complexity of Prenex Separation Logic with One Selector." arXiv:1804.03556 (2018). https://pith.science/paper/QZPALHVI
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What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.80 · compares with prior results 0.11 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite and infinite satisfiability problem for the class of prenex formulas of $\seplogk{1}$, by reduction to the first-order theory of one unary function symbol and unary predicate symbols. We also prove that the complexity is not elementary, by reduction from the first-order theory of one unary function symbol. Finally, we prove that the Bernays-Sch\"onfinkel-Ramsey fragment of prenex $\seplogk{1}$ formulae with quantifier prefix in the language $\exists^*\forall^*$ is \pspace-complete. The definition of a complete (hierarchical) classification of the complexity of prenex $\seplogk{1}$, according to the quantifier alternation depth is left as an open problem.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). result 0.83 0.94 0.17 asserted 1.00
s1 Second, we show that this entails the decidability of the finite and infinite satisfiability problem for the class of prenex formulas of $\seplogk{1}$, by reduction to the first-order theory of one unary function symbol and unary predicate symbols. result 0.88 0.95 0.41 asserted 1.00
s2 We also prove that the complexity is not elementary, by reduction from the first-order theory of one unary function symbol. result 0.98 0.93 0.19 asserted 1.00
s3 Finally, we prove that the Bernays-Sch\"onfinkel-Ramsey fragment of prenex $\seplogk{1}$ formulae with quantifier prefix in the language $\exists^*\forall^*$ is \pspace-complete. result 0.97 0.94 0.15 asserted 1.00
s4 The definition of a complete (hierarchical) classification of the complexity of prenex $\seplogk{1}$, according to the quantifier alternation depth is left as an open problem. future work 0.69 0.15 0.06 asserted 0.79

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite and infinite satisfiability problem for the class of prenex formulas of $\seplogk{1}$, by reduction to the first-order theory of one unary function symbol and unary predicate symbols. We also prove that the complexity is not elementary, by reduction from the first-order theory of one unary function symbol. Finally, we prove that the Bernays-Sch\"onfinkel-Ramsey fragment of prenex $\seplogk{1}$ formulae with quantifier prefix in the language $\exists^*\forall^*$ is \pspace-complete. The definition of a complete (hierarchical) classification of the complexity of prenex $\seplogk{1}$, according to the quantifier alternation depth is left as an open problem.

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