SPDL Model Checking via Property-Driven State Space Generation

In this report we describe how both, memory and time requirements for stochastic model checking of SPDL (stochastic propositional dynamic logic) formulae can significantly be reduced. SPDL is the stochastic extension of the multi-modal program logic PDL.\ud SPDL provides means to specify path-based properties with or without timing restrictions. Paths can be characterised by so-called programs, essentially regular expressions, where the executability can be made dependent on the validity of test formulae. For model-checking SPDL path formulae it is necessary to build a product transition system (PTS)\ud between the system model and the program automaton belonging to the path formula that is to be verified.\ud In many cases, this PTS can be drastically reduced during the model checking procedure, as the program restricts the number of potentially satisfying paths. Therefore, we propose an approach that directly generates the reduced PTS from a given SPA specification and an SPDL path formula.\ud The feasibility of this approach is shown through a selection of case studies, which show enormous state space reductions, at no increase in generation time.\u

Comparison of Implicit Path Enumeration and Model Checking Based WCET Analysis

In this paper, we present our new worst-case execution time (WCET) analysis tool for Java processors, supporting both implicit path enumeration (IPET) and model checking based execution time estimation. Even though model checking is significantly more expensive than IPET, it simplifies accurate modeling of pipelines and caches. Experimental results using the UPPAAL model checker indicate that model checking is fast enough for typical tasks in embedded applications, though large loop bounds may lead to long analysis times. To obtain a tool which is able to cope with larger applications, we recommend to use model checking for more important code fragments, and combine it with the IPET approach

Model Checking Markov Chains with Actions and State Labels

In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure

Path Queries on Compressed XML

Central to any XML query language is a path language such as XPath which operates on the tree structure of the XML document. We demonstrate in this paper that the tree structure can be e#ectively compressed and manipulated using techniques derived from symbolic model checking . Specifically, we show first that succinct representations of document tree structures based on sharing subtrees are highly e#ective. Second, we show that compressed structures can be queried directly and e#ciently through a process of manipulating selections of nodes and partial decompression

Extending the Logic IM-SPDL with Impulse and State Rewards

This report presents the logic SDRL (Stochastic Dynamic Reward Logic), an extension of the stochastic logic IM-SPDL, which supports the specication of complex performance and dependability requirements. SDRL extends IM-SPDL with the possibility to express impulse- and state reward measures.\ud The logic is interpreted over extended action-based Markov reward model (EMRM), i.e. transition systems containing both immediate and Markovian transitions, where additionally the states and transitions can be enriched with rewards.\ud We define ne the syntax and semantics of the new logic and show that SDRL provides powerful means to specify path-based properties with timing and reward-based restrictions.\ud In general, paths can be characterised by regular expressions, also called programs, where the executability of a program may depend on the validity of test formulae. For the model checking of SDRL time- and reward-bounded path formulae, a deterministic program automaton is constructed from the requirement. Afterwards the product transition\ud system between this automaton and the EMRM is built and subsequently transformed into a continuous time Markov reward model (MRM) on which numerical\ud analysis is performed.\u

Global model checking on pushdown multi-agent systems

Pushdown multi-agent systems, modeled by pushdown game structures (PGSs), are an important paradigm of infinite-state multi-agent systems. Alternating-time temporal logics are well-known specification formalisms for multi-agent systems, where the selective path quantifier is introduced to reason about strategies of agents. In this paper, we investigate model checking algorithms for variants of alternating-time temporal logics over PGSs, initiated by Murano and Perelli at IJCAI'15. We first give a triply exponential-time model checking algorithm for ATL* over PGSs. The algorithm is based on the saturation method, and is the first global model checking algorithm with a matching lower bound. Next, we study the model checking problem for the alternating-time mu-calculus. We propose an exponential-time global model checking algorithm which extends similar algorithms for pushdown systems and modal mu-calculus. The algorithm admits a matching lower bound, which holds even for the alternation-free fragment and ATL

Modeling assembly program with constraints. A contribution to WCET problem

Dissertação para obtenção do Grau de Mestre em Lógica ComputacionalModel checking with program slicing has been successfully applied to compute Worst Case Execution Time (WCET) of a program running in a given hardware. This method lacks path feasibility analysis and suffers from the following problems: The model checker (MC) explores exponential number of program paths irrespective of their feasibility. This limits the scalability of this method to multiple path programs. And the witness trace returned by the MC corresponding to WCET may not be feasible (executable). This may result in a solution which is not tight i.e., it overestimates the actual WCET. This thesis complements the above method with path feasibility analysis and addresses these problems. To achieve this: we first validate the witness trace returned by the MC and generate test data if it is executable. For this we generate constraints over a trace and solve a constraint satisfaction problem. Experiment shows that 33% of these traces (obtained while computing WCET on standard WCET benchmark programs) are infeasible. Second, we use constraint solving technique to compute approximate WCET solely based on the program (without taking into account the hardware characteristics), and suggest some feasible and probable worst case paths which can produce WCET. Each of these paths forms an input to the MC. The more precise WCET then can be computed on these paths using the above method. The maximum of all these is the WCET. In addition this, we provide a mechanism to compute an upper bound of over approximation for WCET computed using model checking method. This effort of combining constraint solving technique with model checking takes advantages of their strengths and makes WCET computation scalable and amenable to hardware changes. We use our technique to compute WCET on standard benchmark programs from M¨alardalen University and compare our results with results from model checking method

On-the-Fly Model Checking for Extended Action-Based Probabilistic Operators

International audienceThe quantitative analysis of concurrent systems requires expressive and user-friendly property languages combining temporal, data-handling, and quantitative aspects. In this paper, we aim at facilitating the quantitative analysis of systems modeled as PTSs (Probabilistic Transition Systems) labeled by actions containing data values and probabilities. We propose a new regular probabilistic operator that computes the probability measure of a path specified by a generalized regular formula involving arbitrary computations on data values. This operator, which subsumes the Until operators of PCTL and their action-based counterparts, can provide useful quantitative information about paths having certain (e.g., peak) cost values. We integrated the regular probabilistic operator into MCL (Model Checking Language) and we devised an associated on-the-fly model checking method, based on a combined local resolution of linear and Boolean equation systems. We implemented the method in the EVALUATOR model checker of the CADP toolbox and experimented it on realistic PTSs modeling concurrent systems