On the Combination of the Bernays–Schönfinkel–Ramsey Fragment with Simple Linear Integer Arithmetic

Horbach, Matthias; Voigt, Marco; Weidenbach, Christoph

doi:10.1007/978-3-319-63046-5_6

Cited by 9 publications

(8 citation statements)

References 21 publications

(58 reference statements)

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“…Simpler Forms of Linear Arithmetic: The main logic studied in this paper is obtained by restricting HBS(LA) to a simpler form of linear arithmetic. We first introduce a simpler logic HBS(SLA) as a well-known fragment of HBS(LA) for which satisfiability is decidable [19,22], and later present the generalization HBS(LA) PA of this formalism that we will use. Definition 2.…”

Section: Preliminariesmentioning

confidence: 99%

A Sorted Datalog Hammer for Supervisor Verification Conditions Modulo Simple Linear Arithmetic

Bromberger¹,

Dragoste²,

Faqeh³

et al. 2022

Preprint

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In a previous paper, we have shown that clause sets belonging to the Horn Bernays-Schönfinkel fragment over simple linear real arithmetic (HBS(SLR)) can be translated into HBS clause sets over a finite set of first-order constants. The translation preserves validity and satisfiability and it is still applicable if we extend our input with positive universally or existentially quantified verification conditions (conjectures). We call this translation a Datalog hammer. The combination of its implementation in SPASS-SPL with the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. We verify supervisor code for two examples: a lane change assistant in a car and an electronic control unit of a supercharged combustion engine.In this paper, we improve our Datalog hammer in several ways: we generalize it to mixed real-integer arithmetic and finite first-order sorts; we extend the class of acceptable inequalities beyond variable bounds and positively grounded inequalities; and we significantly reduce the size of the hammer output by a soft typing discipline. We call the result the sorted Datalog hammer. It not only allows us to handle more complex supervisor code and to model already considered supervisor code more concisely, but it also improves our performance on real world benchmark examples. Finally, we replace the before file-based interface between SPASS-SPL and VLog by a close coupling resulting in a single executable binary.

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Section: Preliminariesmentioning

confidence: 99%

A Sorted Datalog Hammer for Supervisor Verification Conditions Modulo Simple Linear Arithmetic

Bromberger¹,

Dragoste²,

Faqeh³

et al. 2022

Preprint

Self Cite

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“…Integer numbers represent sensor input or calibration data of the supervisor. The resulting logic can be viewed (i) as an extension of basic datalog with integer arithmetic, potentially non-Horn rules and unsafe variables [11], (ii) as an extension of SMT (Satisfiability Modulo Theory) by universally quantified variables [36], and (iii) as an instance of function-free first-order logic extended with integer arithmetic [22,43]. Satisfiability in this logic is undecidable in general [23].…”

Section: Superlogmentioning

confidence: 99%

Towards Dynamic Dependable Systems Through Evidence-Based Continuous Certification

Faqeh

Fetzer

Hermanns

et al. 2020

Leveraging Applications of Formal Methods, Verification and Validation: Engineering Principles

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Future cyber-physical systems are expected to be dynamic, evolving while already being deployed. Frequent updates of software components are likely to become the norm even for safety-critical systems. In this setting, a full re-certification before each software update might delay important updates that fix previous bugs, or security or safety issues. Here we propose a vision addressing this challenge, namely through the evidence-based continuous supervision and certification of software variants in the field. The idea is to run both old and new variants of component software inside the same system, together with a supervising instance that monitors their behavior. Updated variants are phased into operation after sufficient evidence for correct behavior has been collected. The variants are required to explicate their decisions in a logical language, enabling the supervisor to reason about these decisions and to identify inconsistencies. To resolve contradictory information, the supervisor can run a component analysis to identify potentially faulty components on the basis of previously observed behavior, and can trigger micro-experiments which plan and execute system behavior specifically aimed at reducing uncertainty. We spell out our overall vision, and provide a first formalization of the different components and their interplay. In order to provide efficient supervisor reasoning as well as automatic verification of supervisor properties we introduce SupERLog, a logic specifically designed to this end.

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“…[20] considered QFBAPA ă 8 , a quantifier-free logic of sets of real numbers supporting integer sets and variables, linear arithmetic, the cardinality operator, infimum and supremum. [32,17] investigated two extensions of the Bernays-Schönfinkel-Ramsey fragment of first-order predicate logic (BSR) with simple linear arithmetic over integers and difference-bound constraints over reals (but crucially, the ranges of the universally quantified variables must be bounded). Since the unary predicate symbols in BSR are uninterpreted and represent sets over integers or reals, the two extensions of BSR can also be used to specify the set constraints on integers or reals.…”

Section: Introductionmentioning

confidence: 99%

Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

Gao

Chen

Zhang

2019

SOFSEM 2019: Theory and Practice of Computer Science

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We identify difference-bound set constraints (DBS), an analogy of difference-bound arithmetic constraints for sets. DBS can express not only set constraints but also arithmetic constraints over set elements. We integrate DBS into separation logic with linearly compositional inductive predicates, obtaining a logic thereof where set data constraints of linear data structures can be specified. We show that the satisfiability of this logic is decidable. A crucial step of the decision procedure is to compute the transitive closure of DBS-definable set relations, to capture which we propose an extension of quantified set constraints with Presburger Arithmetic (RQSPA). The satisfiability of RQSPA is then shown to be decidable by harnessing advanced automata-theoretic techniques.

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On the Combination of the Bernays–Schönfinkel–Ramsey Fragment with Simple Linear Integer Arithmetic

Cited by 9 publications

References 21 publications

A Sorted Datalog Hammer for Supervisor Verification Conditions Modulo Simple Linear Arithmetic

A Sorted Datalog Hammer for Supervisor Verification Conditions Modulo Simple Linear Arithmetic

Towards Dynamic Dependable Systems Through Evidence-Based Continuous Certification

Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

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