Computing Predicate Abstractions by Integrating BDDs and SMT Solvers

Cavada, Roberto; Cimatti, Alessandro; ́en, Anders Franz; Kalyanasundaram, Krishnamani; Roveri, Marco; Shyamasundar, R. K.

doi:10.1109/fmcad.2007.4401984

Cited by 13 publications

(21 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, Damiano and Kukula [16] substitute clauses with BDDs in a DPLL solver, Jin and Somenzi [23] combine BDDs and SAT solving using CNF to avoid explosion in the sizes of the resulting BDDs, whereas Aloul et al [1] study the connection between CNF formulae and BDDs for good variable orderings. The approach of Cavada et al [11] recursively computes quantifications for subtrees, which are then combined; SMT solving ensures consistency of the transformations.…”

Section: Hybrid Methods and Mcmillan's Methodsmentioning

confidence: 99%

Existential Quantification as Incremental SAT

Brauer

King

Kriener

2011

Computer Aided Verification

View full text Add to dashboard Cite

Abstract. This paper presents an elegant algorithm for existential quantifier elimination using incremental SAT solving. This approach contrasts with existing techniques in that it is based solely on manipulating the SAT instance rather than requiring any reengineering of the SAT solver or needing an auxiliary data-structure such as a BDD. The algorithm combines model enumeration with the generation of shortest prime implicants so as to converge onto a quantifier-free formula presented in CNF. We apply the technique to a number of hardware circuits and transfer functions to demonstrate the effectiveness of the method.

show abstract

Section: Hybrid Methods and Mcmillan's Methodsmentioning

confidence: 99%

Existential Quantification as Incremental SAT

Brauer

King

Kriener

2011

Computer Aided Verification

View full text Add to dashboard Cite

show abstract

“…MATHSAT5 is a state-of-the-art SMT solver which supports most of the quantifier-free SMT-LIB theories and their combinations, and provides many other SMT functionalities (like, e.g., unsat-core extraction [Cimatti et al 2011], interpolation ], All-SMT [Cavada et al 2007]). …”

Section: Experimental Evaluationmentioning

confidence: 99%

Optimization Modulo Theories with Linear Rational Costs

Sebastiani

Tomasi

2015

ACM Trans. Comput. Logic

122

View full text Add to dashboard Cite

A Optimization Modulo Theories with Linear Rational Costs ROBERTO SEBASTIANI and SILVIA TOMASI, DISI, University of Trento, ItalyIn the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories of practical interest (e.g., linear arithmetic, arrays, bit-vectors). Surprisingly, little work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any previous work on SMT solvers able to produce solutions which minimize cost functions over arithmetical variables. This is unfortunate, since some problems of interest require this functionality.In the work described in this paper we start filling this gap. We present and discuss two general procedures for leveraging SMT to handle the minimization of linear rational cost functions, combining SMT with standard minimization techniques. We have implemented the procedures within the MathSAT SMT solver. Due to the absence of competitors in the AR, FV and SMT domains, we have experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP), which is closest in spirit to our domain, on sets of problems which have been previously proposed as benchmarks for the latter tools. The results show that our tool is very competitive with, and often outperforms, these tools on these problems, clearly demonstrating the potential of the approach. INTRODUCTIONIn the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into and solved as Satisfiability Modulo Theories (SMT) problems. In the last decade efficient SMT solvers have been developed, that combine the power of modern conflict-driven clause-learning (CDCL) SAT solvers with dedicated decision procedures (TSolvers) for several first-order theories of practical interest like, e.g., those of equality with uninterpreted functions (EUF ), of linear arithmetic over the rationals (LA(Q)) or the integers (LA(Z)), of arrays (AR), of bit-vectors (BV), and their combinations. We refer the reader to [Sebastiani 2007;Barrett et al. 2009] for an overview.Many SMT-encodable problems of interest, however, may require also the capability of finding models that are optimal wrt. some cost function over continuous arithmetical variables. For example, in (SMT-based) planning with resources [Wolfman and Weld 1999] a plan for achieving a certain goal must be found which not only fulfills some resource constraints (e.g. on time, gasoline consumption, among others) but that also minimizes the usage of some of such resources; in SMT-based model checking with timed or hybrid systems (e.g. [Audemard et al. 2002;Audemard et al. 2005]) you may want to find executions which minimize some parameter (e.g. Authors' addresses: Roberto Sebastiani (roberto.sebastiani@unitn.it), Silvia Tomasi (silvia.t...

show abstract

“…To do parametric analyses on HCS, we have modelled it using NuSMV and by adapting the parametric modelling tool [14] built upon NuSMT [11], we have derived the feasibility (not shaded) and infeasibility (shaded) regions for the PTP checker shown in Figure 3.6. The regions for the Audio checker under a hard and firm real-time requirement are also shown in the same figure where driftDelta (denoted as ∆) is introduced to account for the offset time of the local clock compared to the server clock.…”

Section: Parametric Analysismentioning

confidence: 99%

A tag contract framework for modeling heterogeneous systems

Fahrenberg

Legay

2016

Science of Computer Programming

View full text Add to dashboard Cite

In the distributed development of modern IT systems, contracts play a vital role in ensuring interoperability of components and adherence to specifications. The design of embedded systems, however, is made more complex by the heterogeneous nature of components, which are often described using different models and interaction mechanisms. Composing such components is generally not well-defined, making design and verification difficult. Several denotational frameworks have been proposed to handle heterogeneity using a variety of approaches. However, the application of heterogeneous modeling frameworks to contract-based design has not yet been investigated.In this work, we develop an operational model with precise heterogeneous denotational semantics, based on tag machines, that can represent heterogeneous composition, and provide conditions under which composition can be captured soundly and completely. The operational framework is implemented in a prototype tool which we use for experimental evaluation. We then construct a full contract model and introduce heterogeneous composition, refinement, dominance, and compatibility between contracts, altogether enabling a formalized and rigorous design process for heterogeneous systems. Besides, we also develop a generic algebraic method to synthesize or refine a set of contracts so that their composition satisfies a given contract.

show abstract

Computing Predicate Abstractions by Integrating BDDs and SMT Solvers

Cited by 13 publications

References 20 publications

Existential Quantification as Incremental SAT

Existential Quantification as Incremental SAT

Optimization Modulo Theories with Linear Rational Costs

A tag contract framework for modeling heterogeneous systems

Contact Info

Product

Resources

About