HySAT: An efficient proof engine for bounded model checking of hybrid systems

Fränzle, Martin; Herde, Christian

doi:10.1007/s10703-006-0031-0

Cited by 90 publications

(72 citation statements)

References 36 publications

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“…This integration is prototypical, lacking any optimizations like reuse of inferences along the isomorphic copies of the transition relation in a BMC problem [6]. Given the extremely high computational cost of computing an interval enclosure of an ODE, such mechanisms for copying inferences across isomorphic sub-formulae rather than recomputing them should provide large speedups.…”

Section: First Experimental Resultsmentioning

confidence: 99%

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SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems

Eggers

Fränzle

Herde

2008

Lecture Notes in Computer Science

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Abstract. In order to facilitate automated reasoning about large Boolean combinations of non-linear arithmetic constraints involving ordinary differential equations (ODEs), we provide a seamless integration of safe numeric overapproximation of initial-value problems into a SATmodulo-theory (SMT) approach to interval-based arithmetic constraint solving. Interval-based safe numeric approximation of ODEs is used as an interval contractor being able to narrow candidate sets in phase space in both temporal directions: post-images of ODEs (i.e., sets of states reachable from a set of initial values) are narrowed based on partial information about the initial values and, vice versa, pre-images are narrowed based on partial knowledge about post-sets. In contrast to the related CLP(F) approach of Hickey and Wittenberg [10], we do (a) support coordinate transformations mitigating the wrapping effect encountered upon iterating interval-based overapproximations of reachable state sets and (b) embed the approach into an SMT framework, thus accelerating the solving process through the algorithmic enhacements of recent SAT solving technology.

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Section: First Experimental Resultsmentioning

confidence: 99%

“…The next release will thus drastically reduce their frequency through proven methods for reuse of deductions within isomorphic subformulae [6] in order to attain performance competitive with existing tools optimized for the domain.…”

Section: Resultsmentioning

confidence: 99%

SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems

Eggers

Fränzle

Herde

2008

Lecture Notes in Computer Science

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“…These range from SMT [19,25,36], deduction [43], level sets [41], and simulation [24] based to flow-pipe construction based methods. In this paper, we compute time-bounded reachability [18] using flow-pipe construction.…”

Section: Related Workmentioning

confidence: 99%

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Bak

Bogomolov

Althoff

2017

Lecture Notes in Computer Science

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Abstract.A promising technique for the formal verification of embedded and cyber-physical systems is flow-pipe construction, which creates a sequence of regions covering all reachable states over time. Flow-pipe construction methods can check whether specifications are met for all states, rather than just testing using a finite and incomplete set of simulation traces. A fundamental challenge when using flow-pipe construction on high-dimensional systems is the cost of geometric operations, such as intersection and convex hull. We address this challenge by showing that it is often possible to remove the need to perform high-dimensional geometric operations by combining two model transformations, direct time-triggered conversion and dynamics scaling. Further, we prove the overapproximation error in the conversion can be made arbitrarily small. Finally, we show that our transformation-based approach enables the analysis of a drivetrain system with up to 51 dimensions.

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“…x 1 +x 2 + x 3 ≥ 3 represents the same function as the propositional formula x 1 ∧ ¬x 2 ∧ x 3 (we identify propositional formulae with functions). It has been observed that a function can be often represented more compactly as a set of LPBs than as a conjunctive or disjunctive normal form (CNF or DNF) [5][6][7][8]. E.g.…”

Section: Introductionmentioning

confidence: 99%

“…Previous works on LPBs [1,[5][6][7][8] have focused on generalising techniques applied in CNF-based propositional satisfiability solving [12,13,21] to LPBs, emphasising that this is beneficial because of the compactness of LPB representations. Dixon and Ginsberg show that since LPBs are a special case of integer programming, the cutting planes proof system, a standard technique in operations research (OR), can be applied to LPBs.…”

Section: Introductionmentioning

confidence: 99%

On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint

Smaus

2007

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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Abstract. A linear pseudo-Boolean constraint (LPB) is an expression of the form a1 · 1 + . . . + am · m ≥ d, where each i is a literal (it assumes the value 1 or 0 depending on whether a propositional variable xi is true or false) and a1, . . . , am, d are natural numbers. An LPB is a generalisation of a propositional clause, on the other hand it is a restriction of integer linear programming. LPBs can be used to represent Boolean functions more compactly than the well-known conjunctive or disjunctive normal forms. In this paper, we address the question: how much more compactly? We compare the expressiveness of a single LPB to that of related formalisms, and give an algorithm for computing an LPB representation of a given formula if this is possible. Note: This report is the long version of [18] and contains the proofs omitted there for space reasons.

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HySAT: An efficient proof engine for bounded model checking of hybrid systems

Cited by 90 publications

References 36 publications

SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems

SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

On Boolean Functions Encodable as a Single Linear Pseudo-Boolean Constraint

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