Extending Propositional Separation Logic for Robustness Properties

We study an extension of propositional separation logic that can specify robustness properties, such as acyclicity and garbage freedom, for automatic verification of stateful programs with singly-linked lists. We show that its satisfiability problem is PSpace-complete, whereas modest extensions of the logic are shown to be Tower-hard. As separating implication, reachability predicates (under some syntactical restrictions) and a unique quantified variable are allowed, this logic subsumes several PSpace-complete separation logics considered in previous works

Exploring the relation between intuitionistic bi and boolean bi: An unexpected embedding

International audienceThe logic of Bunched Implications, through its intuitionistic version (BI) as well as one of its classical versions called Boolean BI (BBI), serves as a logical basis to spatial or separation logic frameworks. In BI, the logical implication is interpreted intuitionistically whereas it is generally interpreted classically in spatial or separation logics like in BBI. In this paper, we aim at giving some new insights w.r.t. the semantic relations between BI and BBI. Then we propose a sound and complete syntactic constraints based framework for Kripke semantics of both BI and BBI, a sound labelled tableau proof system for BBI, and a representation theorem relating the syntactic models of BI to those of BBI. Finally we deduce, as main and unexpected result, a sound and faithful embedding of BI into BBI

The Expressive Power, Satisfiability and Path Checking Problems of MTL and TPTL over Non-Monotonic Data Words

Recently, verification and analysis of data words have gained a lot of interest. Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are two extensions of Linear time temporal logic (LTL). In MTL, the temporal operator are indexed by a constraint interval. TPTL is a more powerful logic that is equipped with a freeze formalism. It uses register variables, which can be set to the current data value and later these register variables can be compared with the current data value. For monotonic data words, Alur and Henzinger proved that MTL and TPTL are equally expressive and the satisfiability problem is decidable. We study the expressive power, satisfiability problems and path checking problems for MLT and TPTL over all data words. We introduce Ehrenfeucht-Fraisse games for MTL and TPTL. Using the EF-game for MTL, we show that TPTL is strictly more expressive than MTL. Furthermore, we show that the MTL definability problem that whether a TPTL-formula is definable in MTL is not decidable. When restricting the number of register variables, we are able to show that TPTL with two register variables is strictly more expressive than TPTL with one register variable. For the satisfiability problem, we show that for MTL, the unary fragment of MTL and the pure fragment of MTL, SAT is not decidable. We prove the undecidability by reductions from the recurrent state problem and halting problem of two-counter machines. For the positive fragments of MTL and TPTL, we show that a positive formula is satisfiable if and only it is satisfied by a finite data word. Finitary SAT and infinitary SAT coincide for positive MTL and positive TPTL. Both of them are r.e.-complete. For existential TPTL and existential MTL, we show that SAT is NP-complete. We also investigate the complexity of path checking problems for TPTL and MTL over data words. These data words can be either finite or infinite periodic. For periodic words without data values, the complexity of LTL model checking belongs to the class AC^1(LogDCFL). For finite monotonic data words, the same complexity bound has been shown for MTL by Bundala and Ouaknine. We show that path checking for TPTL is PSPACE-complete, and for MTL is P-complete. If the number of register variables allowed is restricted, we obtain path checking for TPTL with only one register variable is P-complete over both infinite and finite data words; for TPTL with two register variables is PSPACE-complete over infinite data words. If the encoding of constraint numbers of the input TPTL-formula is in unary notation, we show that path checking for TPTL with a constant number of variables is P-complete over infinite unary encoded data words. Since the infinite data word produced by a deterministic one-counter machine is periodic, we can transfer all complexity results for the infinite periodic case to model checking over deterministic one-counter machines

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Adjuncts elimination in the static ambient logic

The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistructured data. SAL also includes the non-standard fresh quantifier (I). This work adresses the questions of expressiveness and minimality of SAL from the point of view of adjuncts. We define the intensional fragment of the logic (SALint), the logic without adjuncts, and prove that it captures all the expressiveness of the logic. We moreover study the question of adjuncts elimination in SAL ∀ , where I quantifier is replaced by the classical ∀ quantifier. We conclude with a proof of the minimality of SALint