Ong oxford university computing laboratory abstract we prove that the modal mu calculus model checking problem for ranked and ordered nodelabelled trees that are generated by order recursion schemes whether safe or not, and whether homogeneously typed or not is. Xmc is written in under 200 lines of xsb code, which constitute a declarative specification of ccs and the modal mu calculus at the level of semantic equations. As for linear temporal logic, model checking, satisfiability and validity problems of linear modal. Unfortunately, the corresponding decidability procedure is not practical due to its. Mucalculus path checking information processing letters. Model checking games for the alternation free mucalculus and. In computer science, model checking or property checking is a method for checking whether a finitestate model of a system meets a given specification a. Largely used to prove hardware systems correct, new techniques allow its use also to verify.
Automated software engineering journal, special issue on automated software analysis 61. Vis integrates model checking with logic synthesis and simulation. It is a logic with an exceptional balance between expressiveness and algorithmic properties. The other probabilistic calculus was introduced in cleaveland et al. In this paper, we propose to use mu calculus to describe and analyze, using model checking techniques, dynamic data such as lists, and nonlinear data structures like trees.
Because of its expressiveness, model checking algorithms have been extensively investigated for the mu calculus and various of its fragments and94,bc96,cs93,el86,lbcj94. Stanfords step system combines model checking with deductive methods. Furthermore, it separates refinement determination from the 3valued based model checking. The overflow blog socializing with coworkers while social distancing. On modelchecking trees generated by higherorder recursion. Of course, there are algorithms that can do that for us, but we have not discussed them in vrs, since it would lead us to further topics like.
Request pdf on researchgate model checking and the mucalculus. Model checking is a technique to prove a concurrent system finite model satisfies a given property. Ong aoxford university computing laboratory, wolfson building, parks road, oxford ox1 3qd, uk abstract we present an algorithm for computing directly the denotation of a modal calculus formula. May 19, 2018 this chapter presents that part of the theory of the \\ mu \ calculus that is relevant to the model checking problem as broadly understood. Specifications are written in propositional temporal logic. A fixpoint calculus for local and global program flows. This is typically associated with hardware or software systems, where the specification contains liveness requirements as well as safety requirements. Extending model checking techniques to handle realtime programs model checking techniques for the mu calculus model checking for software and static analysis. Therefore the present result, namely that it is possible to model check quantitative calculus on initialised linear hybrid systems, properly generalises a previous result on model checking ltl on such systems 14, 15, which is one of the strongest modelchecking.
The \\ mu \ calculus is one of the most important logics in model checking. As our daily lives depend increasingly on digital systems, the reliability of these systems becomes a concern of overwhelming importance, and as the complexity of the systems grows, their. In its current form, temporal properties are specified in the alternationfree fragment of the modal mu calculus koz83, and system models are specified in xl, a valuepassing language based on ccs mil89. Hottest mucalculus answers theoretical computer science.
One of the bene ts of restricting ourselves to lineartime logic as opposed to a more expressive logic such as ctl or the modal mucalculus is the ability to invoke the magic compositional. Model checking is a successful technique for automatically verifying concurrent finitestate systems. The fragment allows free variables within the scope of. Probabilistic temporal logics via the modal mucalculus. Finally, the chapter discusses the relation of the \mucalculus to monadic second order logic as well as to some program and temporal logics. In this paper we present a local model checker for the mucalculus. Model checking concerns the use of algorithmic methods in the temporal safety and performance assurance for software and hardware systems.
The \\mu\calculus is one of the most important logics in model checking. On model checking trees generated by higherorder recursion schemes c. Compositionality and locality for improving model checking in. Temporal logic model checking model checking is an automatic verification technique for finite state concurrent systems. Uncovering the main research themes of software validation. Eclipse java spin abstraction algorithms explicit model checking formal methods formal specification modal verification modeling mu calculus software verification spin model checking structured. It is based on a more expressive abstract model and applies refinement only locally at a single abstract state, i.
Selective mucalculus in the model checking framework, systems can be represented by transition systems and requirements are expressed as formulae in a temporal logic. Efficient onthefly modelchecking for regular alternation. When system models include probabilistic information regarding their execu. Selective mucalculus logic in this paper we use the selective mucalculus, introduced in 3, which is a branching temporal logic to express behavioral properties of systems. Verification of dynamic data tree with mucalculus extended. We present an approach for familybased verification based on the feature mu calculus mu lf, which combines modalities with feature expressions. A desirable aspect of some such proof systems is that they may be for mulated so as to be \compositional, which facilitates development of a program hand in. Citeseerx fast mucalculus model checking when treewidth. In this case study we define a modelchecker for the mucalculus in acl2 and show how to translate ctl into the mucalculus. A saturation method for the modal mucalculus over pushdown. A saturation method for the modal mucalculus over pushdown systems m. Its main mode of verification is temporallogic model checking ces86, although equivalence checkers have also been implemented.
He constructed a transformation of a higherorder program into a recursion. To this end, we develop new techniques for the discretisation of continuous state spaces based on a special class of strategies in modelchecking games and present a reduction to a class of counter parity games. This article lists model checking tools and gives a synthetic overview their functionalities. Model checking algorithms are used to decide if a finitestate system satisfies a temporal logic formula. A simple probabilistic extension of modal mucalculus. Modelchecking algorithms are used to decide if a finitestate system satisfies a temporal logic formula. A type system equivalent to the modal mucalculus model. In addition, the algorithm that decides the mu calculus is used for symbolic bddbased model checking, a technique that has greatly extended the. In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. Branching time logic strikes back, emerson and lei, 1985.
V ariant formulations of the model checking problem stipulate calculating the set. In addition, the algorithm that decides the mucalculus is used for symbolic bddbased modelchecking, a technique that has greatly extended the applicability of modelchecking. Model checking for mobile android malware evolution. One of the bene ts of restricting ourselves to lineartime logic as opposed to a more expressive logic such as ctl or the modal mucalculus is the ability to invoke the magic compositional abstraction re nement procedures developed for. Thus model checkers accept two inputs, a transition system and a formula, and return true if the formula is satis. Weberlocal parallel model checking for the alternationfree mu calculus proceedings of the 9th international spin workshop on model checking of software spin02, volume 2318 of lncs, springerverlag inc 2002, pp. Students often wonder how one can translate general ctl formulas to calculus. Surprisingly, restricting to deterministic structures does not allow for more efficient model checking algorithm, as we prove tha. This is typically associated with hardware or software systems, where the specification contains liveness requirements such as avoidance of livelock as well as safety requirements such as avoidance of states representing.
The mu calculus is discussed and its complexity is analysed. Transformations of the mu calculus model checking problem to the frameworks of boolean equation systems and parity games are addressed, combined with advanced algorithms for solving the latter artefacts. Finally, the chapter discusses the relations of the mucalculus to monadic second order logic as well as to some program and temporal logics. The pvs theorem prover has a model checker for model mucalculus. When designing a model checker, a good compromise must be made between the expressive power of the property description formalism, the complexity of the model checking problem, and the userfriendliness of the interface. The expressiveness of mu calculus makes it possible to naturally describe these structures. Model checking and the mucalculus request pdf researchgate. Modal specifications are a syntactic fragment of the mu calculus. Citeseerx citation query model checking the java meta.
A further extension of calculus was proposed in mio, 2012a, which is able to encode the full pctl. In proceedings of the 1st annual symposium on logic in computer science. The variable c1 c2 of program one two may take the values 0, 1 or 2. Refining model checking by abstract interpretation. Berkeleys hsis combines model checking with language inclusion. Stateevent based software model checking 3 the stateeventbased formalism presented in this paper is suitable for both sequential and concurrent systems. Model checking games for the alternation free mucalculus. Developed independently by clarke and emerson and by queille and sifakis in early 1980s.
In particular, we present xmc, an xsbbased local model checker for a ccslike valuepassing language and the alternationfree fragment of the modal mu calculus. Model checking software 12th international spin workshop, san francisco, ca, usa, august 2224, 2005. Home browse by title books computeraided reasoning. Verification procedure is an exhaustive search of the state. Then we explain that the efficient nonemptiness procedure for 1swaba presented in \citebvw94 can also be. This chapter presents that part of the theory of the \\mu\calculus that is relevant to the modelchecking problem as broadly understood. Ong has previously shown that the modal mucalculus model checking of trees. An integration of modelchecking with automated proof. In el86 we introduced the idea of model checking for the mucalculus in. Familybased model checking targets the simultaneous verification of multiple system variants, a technique to handle featurebased variability that is intrinsic to software product lines spls. However, the model checking and satisfiability algorithms are still unknown for these calculi and are far from trivial mio, 2012b. In computer science, model checking or property checking is a method for checking whether a finitestate model of a system meets a given specification. More than 40 million people use github to discover, fork, and contribute to over 100 million projects. We show that the model checking problem is decidable for a fragment of the epistemic \ mu calculus.
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