Computing Optimized Representations for Non-convex Polyhedra by Detection and Removal of Redundant Linear Constraints

Scholl, Christoph; Disch, Stefan; Pigorsch, Florian; Kupferschmid, Stefan

doi:10.1007/978-3-642-00768-2_32

Cited by 10 publications

(13 citation statements)

References 21 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This could enable the identification and the removal of redundant constraints in other domains, such as CSP [12,10,9], SMT [35], and Ontologies [19]. This is the subject of future work.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

On Computing Minimal Equivalent Subformulas

Belov

Janota

Lynce

et al. 2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. A propositional formula in Conjunctive Normal Form (CNF) may contain redundant clauses -clauses whose removal from the formula does not affect the set of its models. Identification of redundant clauses is important because redundancy often leads to unnecessary computation, wasted storage, and may obscure the structure of the problem. A formula obtained by the removal of all redundant clauses from a given CNF formula F is called a Minimal Equivalent Subformula (MES) of F. This paper proposes a number of efficient algorithms and optimization techniques for the computation of MESes. Previous work on MES computation proposes a simple algorithm based on iterative application of the definition of a redundant clause, similar to the well-known deletionbased approach for the computation of Minimal Unsatisfiable Subformulas (MUSes). This paper observes that, in fact, most of the existing algorithms for the computation of MUSes can be adapted to the computation of MESes. However, some of the optimization techniques that are crucial for the performance of the state-of-the-art MUS extractors cannot be applied in the context of MES computation, and thus the resulting algorithms are often not efficient in practice. To address the problem of efficient computation of MESes, the paper develops a new class of algorithms that are based on the iterative analysis of subsets of clauses. The experimental results, obtained on representative problem instances, confirm the effectiveness of the proposed algorithms. The experimental results also reveal that many CNF instances obtained from the practical applications of SAT exhibit a large degree of redundancy.

show abstract

“…This could enable the identification and the removal of redundant constraints in other domains, such as CSP [12,10,9], SMT [35], and Ontologies [19]. This is the subject of future work.…”

Section: Discussionmentioning

confidence: 99%

“…Besides propositional logic formulas, the problem of the identification of redundant constraints is relevant in other domains. Concrete examples include Constraint Satisfaction Problems (CSP) [12,10,9], Satisfiability Modulo Theories (SMT) [35], and Ontologies [19].…”

Section: Introductionmentioning

confidence: 99%

On Computing Minimal Equivalent Subformulas

Belov

Janota

Lynce

et al. 2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Typically such models are aimed to verify the code of computerized control systems, with a very modest modeling of the external environment. The major preoccupation in these efforts is in combining the continuous part with techniques, such as BDD or SAT, for handling large discrete state-spaces [7,16].…”

Section: Introductionmentioning

confidence: 99%

SpaceEx: Scalable Verification of Hybrid Systems

Frehse

Guernic

Donzé

et al. 2011

Lecture Notes in Computer Science

707

671

View full text Add to dashboard Cite

Abstract. We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic dynamics. It combines polyhedra and support function representations of continuous sets to compute an over-approximation of the reachable states. The algorithm improves over previous work by using variable time steps to guarantee a given local error bound. In addition, we propose an improved approximation model, which drastically improves the accuracy of the algorithm. The algorithm is implemented as part of SpaceEx, a new verification platform for hybrid systems, available at spaceex.imag.fr. Experimental results of full fixed-point computations with hybrid systems with more than 100 variables illustrate the scalability of the approach.

show abstract

“…Implementation based on LinAIGs: We have implemented a prototype of the model checking algorithm using LinAIGs [7,21,6] for representing sets of states. LinAIGs are able to provide a compact representation for arbitrary boolean combinations of linear constraints and boolean variables (which of course include the formulas from C b (X, Y )).…”

Section: Model Checking Algorithmmentioning

confidence: 99%

“…Our model checking algorithm uses LinAIGs ('And-Inverter-Graphs with linear constraints') [7,21,6] to describe the state space. LinAIGs provide a fully symbolic representation both for the continuous part (i.e.…”

Section: Introductionmentioning

confidence: 99%

Fully Symbolic Model Checking for Timed Automata

Morbé

Pigorsch

Scholl

2011

Computer Aided Verification

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper we introduce a new formal model, called finite state machines with time (FSMT), to represent real-time systems. We present a model checking algorithm for FSMTs, which works on fully symbolic state sets containing both the clock values and the state variables. In order to verify timed automata (TAs) with our model checking algorithm, we present two different methods to convert TAs to FSMTs. In addition to pure interleaving semantics we can convert TAs to FSMTs having a parallelized interleaving behavior which allows parallelism of transitions causing no conflicts. This can dramatically reduce the number of steps during verification. Our experimental results show that our prototype implementation outperforms the state-of-the-art model checkers UPPAAL and RED.

show abstract

Computing Optimized Representations for Non-convex Polyhedra by Detection and Removal of Redundant Linear Constraints

Cited by 10 publications

References 21 publications

On Computing Minimal Equivalent Subformulas

On Computing Minimal Equivalent Subformulas

SpaceEx: Scalable Verification of Hybrid Systems

Fully Symbolic Model Checking for Timed Automata

Contact Info

Product

Resources

About