Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms

Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events that can be non-exponentially distributed. Within parametric ACTMCs, the parameters of alarm-event distributions are not given explicitly and can be subject of parameter synthesis. An algorithm solving the $\varepsilon$-optimal parameter synthesis problem for parametric ACTMCs with long-run average optimization objectives is presented. Our approach is based on reduction of the problem to finding long-run average optimal strategies in semi-Markov decision processes (semi-MDPs) and sufficient discretization of parameter (i.e., action) space. Since the set of actions in the discretized semi-MDP can be very large, a straightforward approach based on explicit action-space construction fails to solve even simple instances of the problem. The presented algorithm uses an enhanced policy iteration on symbolic representations of the action space. The soundness of the algorithm is established for parametric ACTMCs with alarm-event distributions satisfying four mild assumptions that are shown to hold for uniform, Dirac and Weibull distributions in particular, but are satisfied for many other distributions as well. An experimental implementation shows that the symbolic technique substantially improves the efficiency of the synthesis algorithm and allows to solve instances of realistic size.Comment: This article is a full version of a paper accepted to the Conference on Quantitative Evaluation of SysTems (QEST) 201

Compositionality for Quantitative Specifications

We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations

Bounded Model Checking for Parametric Timed Automata

Abstract. The paper shows how bounded model checking can be ap-plied to parameter synthesis for parametric timed automata with con-tinuous time. While it is known that the general problem is undecidable even for reachability, we show how to synthesize a part of the set of all the parameter valuations under which the given property holds in a model. The results form a complete theory which can be easily applied to parametric verification of a wide range of temporal formulae – we present such an implementation for the existential part of CTL −X. 1 Introduction and related work The growing abundance of complex systems in real world, and their presence in critical areas fuels the research in formal specification and analysis. One of the established methods in systems verification is model checking, where the system is abstracted into the algebraic model (e.g. various versions of Kripke structures

Diagnosis using Unfoldings of Parametric Time Petri Nets

Abstract. This paper considers the model of Time Petri Nets (TPNs) extended with time parameters and its use to perform on-line diagnosis of distributed systems. We propose to base the method on unfoldings. Given a partial observation, as a possibly structured set of actions, our method determines the causal relation between events in the model that explain the observation. It can also synthesize parametric constraints associated with these explanations. The method is implemented in the tool Romeo. We present its application to the diagnosis of the example of a cowshed with pigs

Symbolic unfolding of parametric stopwatch petri nets

Abstract. This paper proposes a new method to compute symbolic unfoldings for safe Stopwatch Petri Nets (SwPNs), extended with time parameters, that symbolically handle both the time and the parameters. We propose a concurrent semantics for (parametric) SwPNs in terms of timed processes à la Aura and Lilius. We then show how to compute a symbolic unfolding for such nets, as well as, for the subclass of safe time Petri nets, how to compute a finite complete prefix of this unfolding. Our contribution is threefold: unfolding in the presence of stopwatches or parameters has never been addressed before. Also in the case of time Petri nets, the proposed unfolding has no duplication of transitions and does not require read arcs and as such its computation is more local. Finally the unfolding method is implemented (for time Petri nets) in the tool Romeo

Parametric Verification: An Introduction

This is the author version of the manuscript of the same name published in the Transactions on Petri Nets and Other Models of Concurrency (ToPNoC). This work is partially supported by the ANR national research program PACS (ANR-14-CE28-0002)International audienceThis paper constitutes a short introduction to parametric verification of concurrent systems. It originates from two 1-day tutorial sessions held at the Petri nets conferences in Toru\'n (2016) and Zaragoza (2017). The paper presents not only the basic formal concepts tackled in the video version, but also an extensive literature to provide the reader with further references covering the area. We first introduce motivation behind parametric verification in general, and then focus on different models and approaches, for verifying several kinds of systems. They include Parametric Timed Automata, for modelling real-time systems, where the timing constraints are not necessarily known a priori. Similarly, Parametric Interval Markov Chains allow for modelling systems where probabilities of events occurrences are intervals with parametric bounds. Parametric Petri Nets allow for compact representation of systems, and cope with different types of parameters. Finally, Action Synthesis aims at enabling or disabling actions in a concurrent system to guarantee some of its properties. Some tools implementing these approaches were used during hands-on sessions at the tutorial. The corresponding practicals are freely available on the Web