Quantifier Elimination by Lazy Model Enumeration

Monniaux, David

doi:10.1007/978-3-642-14295-6_51

Cited by 53 publications

(70 citation statements)

References 16 publications

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“…3.2]. More recently, Monniaux [30] described a method for quantifier elimination called lazy model enumeration. The key idea of his algorithm is to derive a cube that implies a given formula, which is then generalised towards a weaker implicant.…”

Section: Methods Based On Primes and Cubesmentioning

confidence: 99%

Existential Quantification as Incremental SAT

Brauer

King

Kriener

2011

Computer Aided Verification

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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.

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Section: Methods Based On Primes and Cubesmentioning

confidence: 99%

Existential Quantification as Incremental SAT

Brauer

King

Kriener

2011

Computer Aided Verification

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“…This is why QE for linear fragments of integer and real theories has been a very busy research domain. The most recent advance for linear QE combines state of the art SMT-solving with polyhedral projection [15] for a great performance increase, the general idea of which is given in Algorithm 1.…”

Section: Smt-based Verification Approachesmentioning

confidence: 99%

Formal Methods for the Analysis of Critical Control Systems Models: Combining Non-Linear and Linear Analyses

Champion¹,

Delmas²,

Dierkes³

et al. 2013

SAE Int. J. Aerosp.

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Abstract. Critical control systems are often built as a combination of a control core with safety mechanisms allowing to recover from failures. For example a PID controller used with triplicated inputs and voting. Typically these systems would be designed at the model level in a synchronous language like Lustre or Simulink, and their code automatically generated from these models. We present a new analysis framework combining the analysis of open-loop stable controllers with safety constructs (redundancy, voters, ...). We introduce the basic analysis approaches: abstract interpretation synthesizing quadratic invariants and backward analysis based on quantifier elimination and convex hull computation synthesizing linear invariants. Then we apply it on a simple but representative example that no other available state-of-the-art technique is able to analyze. This contribution is another step towards early use of formal methods for critical embedded software such as the ones of the aerospace industry. Control-Command Software Focused Analyses to Address V&V and Certification NeedsThe aerospace industry is notoriously faced with highly critical issues. The safety of systems should be guaranteed even if the cost of ensuring safety is important. In development costs of the Boeing 777 [8], software accounts for a third of all costs. In this third, 70% consists in verification costs while only 30% are devoted to software development. Other aircraft manufacturers have similar figures. The software specific certification regulatory document, ie. the recently updated DO 178-C, characterizes different levels of criticality from level A -the most critical -to level E -the less critical. Depending on the identified level, verification and validation activities are more or less intensive and therefore costly. This certification document has recently been updated and it also provides a formal methods supplement, identified as RTCA DO 333. This supplement explicitly enables the use of formal methods for critical embedded software.Among the various systems of an aircraft, and their associated software, one of the most critical is the flight control system of the aircraft. Addressing the issue of verifying such specific software seems to be a pertinent goal: proposing 2 A. Champion, R. Delmas, M. Dierkes, P.L. Garoche, P. Roux new ways to validate it could both increase the trust we have in the released software and reduce the cost of V & V by providing more automatic (and exhaustive) analysis means.These reactive system can be seen as the composition of two parts. The first is the computation core itself, achieving the main objective of the software: controlling the aircraft by receiving inputs from sensors and commanding the aircraft actuators. The second part tries to handle any possible failure of sensors or of the core system. This safety architecture is mainly based on information redundancy and fusion. These two parts are usually designed using a model based approach.The approach of control system modeling as proposed by The...

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“…Indeed, transforming a propositional formula into an equivalent formula in disjunctive normal form may cause an exponential blow-up. A more advanced improvement of Cooper's procedure can be found in [RL78]; recent developments propose a lazy approach to quantifier elimination [Mon10].…”

Section: How To Deal With Quantifiersmentioning

confidence: 99%

“…Even though Presburger arithmetic admits quantifier elimination, it is known that eliminating quantifiers can be computationally expensive (see e.g., [RL78,Grä88]). Recent developments propose a promising, lazy approach for quantifier elimination [Mon10].…”

Section: Introductionmentioning

confidence: 99%

Witness Runs for Counter Machines

Barrett

Demri

Deters

2013

Frontiers of Combining Systems

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Abstract. In this paper, we present recent results about the verification of counter machines by using decision procedures for Presburger arithmetic. We recall several known classes of counter machines for which the reachability sets are Presburger-definable as well as temporal logics with arithmetical constraints. We discuss issues related to flat counter machines, path schema enumeration, and the use of SMT solvers.

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Quantifier Elimination by Lazy Model Enumeration

Cited by 53 publications

References 16 publications

Existential Quantification as Incremental SAT

Existential Quantification as Incremental SAT

Formal Methods for the Analysis of Critical Control Systems Models: Combining Non-Linear and Linear Analyses

Witness Runs for Counter Machines

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