A Monte Carlo model checker for probabilistic LTL with numerical constraints

We define the syntax and semantics of a new temporal logic called probabilistic LTL with numerical constraints (PLTLc). We introduce an efficient model checker for PLTLc properties. The efficiency of the model checker is through approximation using Monte Carlo sampling of finite paths through the model’s state space (simulation outputs) and parallel model checking of the paths. Our model checking method can be applied to any model producing quantitative output – continuous or stochastic, including those with complex dynamics and those with an infinite state space. Furthermore, our offline approach allows the analysis of observed (real-life) behaviour traces. We find in this paper that PLTLc properties with constraints over free variables can replace full model checking experiments, resulting in a significant gain in efficiency. This overcomes one disadvantage of model checking experiments which is that the complexity depends on system granularity and number of variables, and quickly becomes infeasible. We focus on models of biochemical networks, and specifically in this paper on intracellular signalling pathways; however our method can be applied to a wide range of biological as well as technical systems and their models. Our work contributes to the emerging field of synthetic biology by proposing a rigourous approach for the structured formal engineering of biological systems

STAMINA: Stochastic Approximate Model-Checker for Infinite-State Analysis

Reliable operation of every day use computing system, from simple coffee machines to complex flight controller system in an aircraft, is necessary to save time, money, and in some cases lives. System testing can check for the presence of unwanted execution but cannot guarantee the absence of such. Probabilistic model checking techniques have demonstrated significant potential in verifying performance and reliability of various systems whose execution are defined with likelihood. However, its inability to scale limits its applicability in practice. This thesis presents a new model checker, STAMINA, with efficient and scalable model truncation for probabilistic verification. STAMINA uses a novel model reduction technique generating a finite state representations of large systems that are amenable to existing probabilistic model checking techniques. The proposed method is evaluated on several benchmark examples. Comparisons with another state-of-art tool demonstrates both accuracy and efficiency of the presented method

Assume-guarantee verification for probabilistic systems

We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour. We adopt an assume- guarantee approach to verification, where both the assumptions made about system components and the guarantees that they provide are regular safety properties, represented by finite automata. Unlike previous proposals for assume-guarantee reasoning about probabilistic systems, our approach does not require that components interact in a fully synchronous fashion. In addition, the compositional verification method is efficient and fully automated, based on a reduction to the problem of multi-objective probabilistic model checking. We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is satisfied. Our techniques have been implemented and applied to several large case studies, including instances where conventional probabilistic verification is infeasible

Efficient Parallel Statistical Model Checking of Biochemical Networks

We consider the problem of verifying stochastic models of biochemical networks against behavioral properties expressed in temporal logic terms. Exact probabilistic verification approaches such as, for example, CSL/PCTL model checking, are undermined by a huge computational demand which rule them out for most real case studies. Less demanding approaches, such as statistical model checking, estimate the likelihood that a property is satisfied by sampling executions out of the stochastic model. We propose a methodology for efficiently estimating the likelihood that a LTL property P holds of a stochastic model of a biochemical network. As with other statistical verification techniques, the methodology we propose uses a stochastic simulation algorithm for generating execution samples, however there are three key aspects that improve the efficiency: first, the sample generation is driven by on-the-fly verification of P which results in optimal overall simulation time. Second, the confidence interval estimation for the probability of P to hold is based on an efficient variant of the Wilson method which ensures a faster convergence. Third, the whole methodology is designed according to a parallel fashion and a prototype software tool has been implemented that performs the sampling/verification process in parallel over an HPC architecture

Interval Change-Point Detection for Runtime Probabilistic Model Checking

Recent probabilistic model checking techniques can verify reliability and performance properties of software systems affected by parametric uncertainty. This involves modelling the system behaviour using interval Markov chains, i.e., Markov models with transition probabilities or rates specified as intervals. These intervals can be updated continually using Bayesian estimators with imprecise priors, enabling the verification of the system properties of interest at runtime. However, Bayesian estimators are slow to react to sudden changes in the actual value of the estimated parameters, yielding inaccurate intervals and leading to poor verification results after such changes. To address this limitation, we introduce an efficient interval change-point detection method, and we integrate it with a state-of-the-art Bayesian estimator with imprecise priors. Our experimental results show that the resulting end-to-end Bayesian approach to change-point detection and estimation of interval Markov chain parameters handles effectively a wide range of sudden changes in parameter values, and supports runtime probabilistic model checking under parametric uncertainty

Practical applications of probabilistic model checking to communication protocols

Probabilistic model checking is a formal verification technique for the analysis of systems that exhibit stochastic behaviour. It has been successfully employed in an extremely wide array of application domains including, for example, communication and multimedia protocols, security and power management. In this chapter we focus on the applicability of these techniques to the analysis of communication protocols. An analysis of the performance of such systems must successfully incorporate several crucial aspects, including concurrency between multiple components, real-time constraints and randomisation. Probabilistic model checking, in particular using probabilistic timed automata, is well suited to such an analysis. We provide an overview of this area, with emphasis on an industrially relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approaches to the implementation of probabilistic model checking, namely those based on numerical computation and those based on discrete-event simulation. Using results from the two tools PRISM and APMC, we summarise the advantages, disadvantages and trade-offs associated with these techniques

Scalable Verification of Markov Decision Processes

Markov decision processes (MDP) are useful to model concurrent process optimisation problems, but verifying them with numerical methods is often intractable. Existing approximative approaches do not scale well and are limited to memoryless schedulers. Here we present the basis of scalable verification for MDPSs, using an O(1) memory representation of history-dependent schedulers. We thus facilitate scalable learning techniques and the use of massively parallel verification.Comment: V4: FMDS version, 12 pages, 4 figure