In this paper, we explore a methodology for generating a Markov chain directly from executable modules in Maude.Initially, we incorporate stochastic parameters in Maude specifications in a straightforward and flexible way.Then, we focus on accurately computing state transition rates, a challenging task due to the complexities introduced by rewriting logic semantics.Our methodology is general and relies on a structured description of states that includes the exact state transition rates.This capability allows for the complete automation of the process, a crucial aspect of our ongoing research.We illustrate this methodology using stochastic rewritable Petri nets, a powerful model for adaptive distributed systems.Finally, we present some preliminary findings based on application examples.106 Capra, L. Associating a Markov Process with Maude Executable Modules.

Modern distributed systems are becoming pervasive and increasingly provided with adaptation, (self-)reconfiguration and mobility capability. On one side, to face the challenges of the highly dynamic environments where they are deployed. On the other side, to keep production/maintenance costs down. Therein lies the increasing demand for formal models encompassing all of these aspects (besides concurrency). Hardly any of the classical formalisms like Petri Nets, Automata, and Process Algebra, even though powerful, permits designers to easily specify dynamic structural changes to systems and evaluate their impact on system behaviour. That has led to several extensions of classical formal models (e.g., the Pi calculus or the Nets-within-Nets paradigm) rarely accompanied by suitable analysis techniques. A recent formalization of a class of Rewritable Place-Transition Nets (RwPT) in Maude has proved potentially convenient to specify dynamically reconfigurable systems. Concerning analogous proposals, the RwPT formalism provides more abstraction/flexibility in modelling and efficiency in analysis. Nevertheless, its ability to scale the size of distributed systems built of several similar (nested) components is limited. This paper presents a compositional approach to define large RwPT models in a typical algebraic way and to exploit the modular structure of models during the analysis: Symmetries are implicitly captured by composite node-labelling (reflecting the model's hierarchical structure) that is preserved by net rewrites. A distributed, gracefully degrading production system is used as a case study. Experimental evidence points out the dramatic impact of the approach against a non-modular one and the advantages over alternative techniques. Even if the emphasis is on state-space-based verification, the paper shows the convenience of combining it with structural analysis, which is typical of Petri nets as well. For that purpose, rewrite-rule abstractions are given in the form of guidelines.

High-level Petri nets (HLPNs) are an expressive formalism well supported by a number of tools that automate the editing and the interactive simulation of models and some kinds of analytical techniques, mainly based on state-space exploration. Structural analysis of HLPNs is, however, a challenging task not yet adequately supported and it is often accomplished via the unfolding of an HLPN into a corresponding low-level Petri Net. An approach to derive a system of Ordinary Differential Equations (ODEs) from a Stochastic Symmetric Net (SSN) has been proposed a few years ago, based on the net's unfolding and subsequent grouping of similar equations. This method has been recently improved by providing an algorithm that directly derives a compact ODE system (from a partially unfolded net) in a symbolic way, through algebraic manipulation of SSN annotations. In this paper, we present the automation of the calculus of Symbolic ODEs (SODEs) for SSN models as a new module of SNexpression, a tool for the symbolic structural analysis of Symmetric Nets. An application of the tool/technique to a variant of a SIRS epidemic model including antibiotic resistance is also described.

Summary The recent extensive availability of ‘cloud’ computing platforms is very appealing for the formal verification community. In fact, these platforms represent a great opportunity to run massively parallel jobs and analyze ‘big data’ problems, although classical formal verification tools and techniques must undergo a deep technological transformation to take advantage of the available powerful architectures. A distributed approach to verification of computation tree logic formulas on very large state spaces is described. The approach exploits and integrates our parametric state–space builder, designed to ease the adoption of ‘big data’ platforms. The whole framework adopts aMAPREDUCEapproach as the core computational model and can be tailored to different modeling formalisms. This paper includes proofs of correctness, a short theoretical discussion about complexity, and reports a practical experience with some benchmarking Petri net models. The outcomes of several tests are presented, thus showing the convenience of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.

The design of evolving discrete-event systems needs for adequate modeling techniques. A Petri net-based reflective layout has been recently proposed to support dynamic discrete event system's design. Keeping functional aspects separated from evolutionary ones, deploying changes to the (current) system configuration when necessary, results in a clean formal model preserving the ability of verifying properties typical of Petri nets. Reflective Petri nets are provided with a pseudo-symbolic state transition graph, and an associated lumped Markov process.

Stochastic well formed colored nets (SWN) make it possible to apply performance evaluation techniques on a compact representation of the reachability graph (RG), called the Symbolic RG (SRG). The Extended SRG (ESRG) has been proposed to achieve a higher degree of reduction when applied to partially symmetric SWN models. The price to pay for the more effective state space reduction, is a loss of information on the paths of the graph. Despite this loss, it has been shown that several qualitative properties can be studied on the ESRG. We consider the possibility of using the ESRG for performance evaluation purposes and more specifically, we explore how the ergodicity of the system can be decided on this graph.

The increasing complexity of automation systems, which combine high functional, real-time and fault-tolerant requirements, demands for techniques and tools to support design choices and validation phases. In this paper we investigate the possibility of using a class of high-level stochastic Petri nets known as stochastic well-formed nets (SWN) as a framework for specifying and deriving quantitative properties of FT mechanisms used in (electric) plant automation. A temporal redundancy technique adopted in several plants is taken as a case-study.