Different directions in parallel and distributed model checking: (invited talk)

The difference in the complexity of branching and linear model checking has been viewed as an argument in favor of the branching paradigm. In particular, the computational advantage of CTL model checking over LTL model checking makes CTL a popular choice, leading to efficient model-checking tools for this logic. Can we use these tools in order to verify linear properties? In this paper we relate branching and linear model checking. With each LTL formula ψ, we associate a CTL formula ψ A that is obtained from ψ by preceding each temporal operator by the universal path quantifier A. We first describe a number of attempts to utilize the tight syntactic relation between ψ and ψ A in order to use CTL model-checking tools in the process of checking the formula ψ. Neither attempt, however, suggests a method that is guaranteed to perform better than usual LTL model checkers. We then claim that, in practice, LTL model checkers perform nicely on formulas with equivalences of CTL. In fact, they often proceed essentially as the ones for CTL.KeywordsModel CheckTemporal LogicLinear Temporal LogicAtomic PropositionLinear Temporal Logic FormulaThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

There are two main paradigms for model checking: symbolic model checking, as is performed by the tool RuleBase, and explicit state model checking, as is performed by Spin. It is often accepted that the former is better for verifying hardware systems, while the latter has advantages for verifying software. We examine this piece of common wisdom in light of experience in verifying the software of a disk controller using both symbolic and explicit state model checking.

In temporal-logic model checking, we verify the correctness of a program with respect to a desired behavior by checking whether a structure that models the program satisfies a temporal-logic formula that specifies the behavior. The model-checking problem for the branching-time temporal logic CTL can be solved in linear running time, and model-checking tools for CTL are used successfully in industrial applications. The development of programs that must meet rigid real-time constraints has brought with it a need for real-time temporal logics that enable quantitative reference to time. Early research on real-time temporal logics uses the discrete domain of the integers to model time. Present research on real-time temporal logics focuses on continuous time and uses the dense domain of the reals to model time. There, model checking becomes significantly more complicated. For example, the model-checking problem for TCTL, a continuous-time extension of the logic CTL, is PSPACE-complete.In this paper we suggest a reduction from TCTL model checking to CTL model checking. The contribution of such a reduction is twofold. Theoretically, while it has long been known that model-checking methods for untimed temporal logics can be extended quite easily to handle discrete time, it was not clear whether and how untimed methods can handle the reset quantifier of TCTL, which resets a realvalued clock. Practically, our reduction enables anyone who has a tool for CTL model checking to use it for TCTL model checking. The TCTL model-checking algorithm that follows from our reduction is in PSPACE, matching the known bound for this problem. In addition, it enjoys the wide distribution of CTL model-checking tools and the extensive and fruitful research efforts and heuristics that have been put into these tools.KeywordsModel CheckTemporal LogicAtomic PropositionKripke StructureTemporal ReasoningThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Although model checking has proven remarkably effective in detecting errors in hardware designs, its success in the analysis of software specifications has been limited. Model checking algorithms for hardware verification commonly use Binary Decision Diagrams (BDDs) to represent predicates involving the many Boolean variables commonly found in hardware descriptions. Unfortunately, BDD representations may be less effective for analyzing software specifications, which usually contain not only Booleans but variables spanning a wide range of data types. Further, software specifications typically have huge, sometimes infinite, state spaces that cannot be model checked directly using conventional symbolic methods. One promising but largely unexplored approach to model checking software specifications is to apply mathematically sound abstraction methods. Such methods extract a reduced model from the specification, thus making model checking feasible. Currently, users of model checkers routinely analyze reduced models but often generate the models in ad hoc ways. As a result, the reduced models may be incorrect. This paper, an expanded version of (Bharadwaj and Heitmeyer, 1997), describes how one can model check a complete requirements specification expressed in the SCR (Software Cost Reduction) tabular notation. Unlike previous approaches which applied model checking to mode transition tables with Boolean variables, we use model checking to analyze properties of a complete SCR specification with variables ranging over many data types. The paper also describes two sound and, under certain conditions, complete methods for producing abstractions from requirements specifications. These abstractions are derived from the specification and the property to be analyzed. Finally, the paper describes how SCR requirements specifications can be translated into the languages of Spin, an explicit state model checker, and SMV, a symbolic model checker, and presents the results of model checking two sample SCR specifications using our abstraction methods and the two model checkers.

Regular model checking is a form of symbolic model checking technique for systems whose states can be represented as finite words over a finite alphabet, where regular sets are used as symbolic representation. A major problem in symbolic model checking of parameterized and infinite-state systems is that fixpoint computations to generate the set of reachable states or the set of reachable loops do not terminate in general. Therefore, acceleration techniques have been developed, which calculate the effect of arbitrarily long sequences of transitions generated by some action. We present a systematic method for using acceleration in regular model checking, for the case where each transition changes at most one position in the word; this includes many parameterized algorithms and algorithms on data structures. The method extracts a maximal (in a certain sense) set of actions from a transition relation. These actions, and systematically obtained compositions of them, are accelerated to speed up a fixpoint computation. The extraction can be done on any representation of the transition relation, e.g., as a union of actions or as a single monolithic transducer. Using this approach, we are for the first time able to verify completely automatically both safety and absence of starvation properties for a collection of parameterized synchronization protocols from the literature; for some protocols, we obtain significant improvements in verification time. The results show that symbolic state-space exploration, without using abstractions, is a viable alternative for verification of parameterized systems with a linear topology.KeywordsModel CheckTransition RelationReachable StateLiveness PropertySymbolic Model CheckThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Abstraction is a fundamental technique that enables the verification of large systems. In symbolic model checking, abstractions are defined by formulas that relate concrete and abstract variables. In predicate abstraction, the abstract variables are equivalent to some predicates over the concrete variables. In order to apply model checking on the abstract state space, it is usually necessary to compute a quantifier-free formula that is equivalent to the abstract transition relation. In predicate abstraction, the quantifier elimination can be obtained by solving an ALLSAT problem. In many practical cases, this computation results into a bottleneck. In this paper, we propose a new algorithm that combines abstraction with bounded model checking and k-induction. The algorithm does not rely on quantifier elimination, but encodes the model checking problem over the abstract state space into SAT problems. The algorithm is a novelty in the state-of-the-art of abstract model checking because it avoids computing the abstraction. An experimental evaluation with case studies taken from an industrial project shows that the new algorithm is more efficient and reaches in some cases a time improvement that is exponential in the number of predicates.

Model checking is widely used in verifying properties of concurrent systems. As an improvement, symbolic model checking uses OBDDs to alleviate the state explosion problem. However, the size of OBDDs greatly increases with the system becoming larger and more complex. In symbolic computation Wu's method is efficient to solve algebraic equations, and has succeeded in geometry theorem proving. In this paper, we present a framework to apply Wu's method to symbolic model checking. Briefly, symbolic model checking is carried out by using Wu's method to calculate the characteristic sets of polynomials that represent Kripke structures as well as CTL formulas. This is a new approach to model checking, and is a new successful application of Wu's method.

We review our progress in high-performance model checking. Our multi-core model checker is based on a scalable hash-table design and parallel random-walk traversal. Our symbolic model checker is based on Multiway Decision Diagrams and the saturation strategy. The LTSmin tool is based on the PINS architecture, decoupling model checking algorithms from the input specification language. Consequently, users can stay in their own specification language and postpone the choice between parallel or symbolic model checking. We support widely different specification languages including those of SPIN (Promela), mCRL2 and UPPAAL (timed automata). So far, multi-core and symbolic algorithms had very little in common, forcing the user in the end to make a wise trade-off between memory or speed. Recently, however, we designed a novel multi-core BDD package called Sylvan. This forms an excellent basis for scalable parallel symbolic model checking.

Workflows have proven to be a useful conceptualization for the automation of business processes. While formal verification methods (e.g., model checking) can help ensure the reliability of workflow systems, the industrial uptake of such methods has been slow largely due to the effort involved in modeling and the memory required to verify complex systems. Incorporation of time constraints in such systems exacerbates the latter problem. We present an automated translator, YAWL2DVE-t, which takes as input a time constrained workflow model built with the graphical modeling tool YAWL, and outputs the model in DVE, the system specification language for the distributed LTL model checker DiVinE. The automated translator, together with the graphical editor and the distributed model checker, provides a method for rapid design, verification and refactoring of time constrained workflow systems. We present a realistic case study developed through collaboration with the local health authority.KeywordsWorkflow SystemsModelingTimeAutomated TranslationDistributed Model Checking

Model checking memoryful linear-time logics over one-counter automata

A parameter generation method based on model checking is proposed to tackle the parameter selection of hierarchical scheduling systems in Integrated Modular Avionics (IMA) by combining the classical symbolic model checking and the Statistical Model Checking (SMC). It builds a generic timed automata network to describe the temporal behavior of hierarchical systems. A distributed genetic algorithm is adopted to search the optimum partition parameters with respect to processor utilization while guaranteeing the schedulability of the system, which is formulated as safety properties of symbolic model checking and hypothesis testing of SMC. Comparing with the widely-used response time analysis, the formal model of this method is more expressive to cover complex features. The application of SMC alleviates the "state space explosion" of classical model checking. Finally, the parameter generation experiments show that the present method is able to find the global optimum solutions in the parameter space.

One of the most debatable features of Event driven Process Chains (EPCs) is their non-local semantics, which results in some difficulties when formalising their semantics. Recently, we have overcome these problems by using techniques from fixed-point theory for defining the semantics of an EPC, which consists of a pair of related transition relations. This fixed-point characterisation of the semantics of EPCs provides a mathematical characterisation of the semantics of EPCs only. For simulating an EPC based on this semantics, we need an efficient way for calculating the corresponding pair of transition relations. A naive implementation of the underlying fixed-point iteration for calculating the transition relations results in a practically useless algorithm. In this paper, we show how to calculate the semantics of an EPC in a more efficient way by employing different techniques and optimisations from symbolic model checking. We also analysed all kinds of simplifications of EPCs to make the calculation of the semantics more efficient, but it turned out that most of these techniques are ineffective. Still, our algorithms are fast enough for simulating practical size EPCs. In order to demonstrate the efficiency of our algorithms and data structures, we have started an open source project called EPC Tools, which could be a good starting point for an open source tool for the EPC community.

In the automata theoretic approach to explicit state LTL model checking, the synchronized product of the model and an automaton that represents the negated formula is checked for emptiness. In practice, a (transition-based generalized) Büchi automaton (TGBA) is used for this procedure. This paper investigates whether using a more general form of acceptance, namely a transition-based generalized Rabin automaton (TGRA), improves the model checking procedure. TGRAs can have significantly fewer states than TGBAs; however, the corresponding emptiness checking procedure is more involved. With recent advances in probabilistic model checking and LTL to TGRA translators, it is only natural to ask whether checking a TGRA directly is more advantageous in practice. We designed a multi-core TGRA checking algorithm and performed experiments on a subset of the models and formulas from the 2015 Model Checking Contest and generated LTL formulas for models from the BEEM database. While we found little to no improvement by checking TGRAs directly, we show how various aspects of a TGRA’s structure influences the model checking performance. In this paper, we also introduce a Fin-less acceptance condition, which is a disjunction of TGBAs. We show how to convert TGRAs into automata with Fin-less acceptance and show how a TGBA emptiness procedure can be extended to check Fin-less automata.

We propose predicate abstraction as a means for verifying a rich class of safety and liveness properties for dense real-time systems. First, we define a restricted semantics of timed systems which is observationally equivalent to the standard semantics in that it validates the same set of mu-calculus formulas without a next-step operator. Then, we recast the model checking problem S |= phi for a timed automaton S and a mu-calculus formula phi in terms of predicate abstraction. Whenever a set of abstraction predicates forms a so-called <em>basis</em>, the resulting abstraction is strongly preserving in the sense that S validates phi iff the corresponding finite abstraction validates this formula phi. Now, the abstracted system can be checked using familiar mu-calculus model checking.<br /> <br />Like the region graph construction for timed automata, the predicate abstraction algorithm for timed automata usually is prohibitively expensive. In many cases it suffices to compute an approximation of a finite bisimulation by using only a subset of the basis of abstraction predicates. Starting with some coarse abstraction, we define a finite sequence of refined abstractions that converges to a strongly preserving abstraction. In each step, new abstraction predicates are selected nondeterministically from a finite basis. Counterexamples from failed mu-calculus model checking attempts can be used to heuristically choose a small set of new abstraction predicates for refining the abstraction.

Game Over: The Foci Approach to LTL Satisfiability and Model Checking