Аппроксимация ресурсных эквивалентностей в сетях Петри с невидимыми переходами

Two resources (submarkings) are called similar if in any marking any one of them can be replaced by another one without affecting the observable behavior of the net (regarding marking bisimulation). It is known that resource similarity is undecidable for general labelled Petri nets. In this paper we study the properties of the resource similarity and resource bisimulation (a subset of complete similarity relation closed under transition firing) in Petri nets with invisible transitions (where some transitions may be labelled with an invisible label (τ) that makes their firings unobservable for an external observer). It is shown that for a proper subclass (p-saturated nets) the resource bisimlation can be effectively checked. For a general class of Petri net with invisible transitions it is possible to construct a sequence of so-called (n, m)-equivalences approximating the largest τ-bisimulation of resources.Два ресурса (подразметки) называются подобными, если в любой разметке любой из них может быть заменен другим, и при этом наблюдаемое поведение сети не изменится (относительно бисимуляции разметок). Известно, что подобие ресурсов неразрешимо для обыкновенных сетей Петри. В этой статье мы изучаем свойства подобия ресурсов и бисимуляции ресурсов (подмножество отношения подобия, замкнутое по срабатыванию переходов) в сетях Петри с невидимыми переходами (где некоторые переходы могут быть помечены специальной меткой (τ), что делает их срабатывания невидимыми для внешнего наблюдателя). Показано, что для собственного подкласса (p-насыщенных сетей) бисимуляция ресурсов может быть эффективно проверена. Для общего класса сетей Петри с невидимыми переходами можно построить последовательность так называемых (n, m)-эквивалентностей, аппроксимирующую наибольшую τ-бисимиляцию ресурсов

Resource Bisimilarity in Petri Nets is Decidable

Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in Petri net models can represent the control flow state or resources produced/consumed by transition firings. We define a resource as a part (submultiset) of the Petri net marking and call two resources equivalent iff replacing one of them with another in any marking does not change the observable Petri net behavior. We investigate the resource similarity and the resource bisimilarity -- congruent restrictions of the bisimulation equivalence on Petri net markings and prove that the resource bisimilarity is decidable in contrast to the resource similarity.Comment: New version for submission to the journa

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

A Comparison of Petri Net Semantics under the Collective Token Philosophy

In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. We use the notion of adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic

Performance Evaluation of Software using Formal Methods

Formal Methods (FMs) can be used in varied areas of applications and to solve critical and fundamental problems of Performance Evaluation (PE). Modelling and analysis techniques can be used for both system and software performance evaluation. The functional features and performance properties of modern software used for performance evaluation has become so intertwined. Traditional models and methods for performance evaluation has been studied widely which culminated into the modern models and methods for system and software engineering evaluation such as formal methods. Techniques have transcended from functionality to performance modeling and analysis. Formal models help in identifying faulty reasoning far earlier than in traditional design; and formal specification has proved useful even on already existing software and systems. Formal approach eliminates ambiguity. The basic and final goal of the performance evaluation technique is to come to a conclusion, whether the software and system are working in a good condition or satisfactorily