Construction of Occurrence Graphs with Permutation Symmetries Aided by the Backtrack Method

This paper recalls the concept of occurrence graphs with permuta- tion symmetries (OS-graphs) for Coloured Petri Nets. It is explained how so-called self-symmetries can help to speed up construction of OS- graphs. The contribution of the paper is to suggest a new method for calculation of self-symmetries, the Backtrack Method. The method is based on the so-called Backtrack Algorithm, which originates in com- putational group theory. The suggestion of the method is justified, both by identifying an important general complexity property and by obtaining encouraging experimental performance measures.Topics. Coloured Petri Nets, reduced state spaces, occurrence graphs with permutation symmetries, self-symmetries, computational group theory, backtrack searches

The Symmetry Method for Coloured Petri Nets

This booklet is the author's PhD-dissertation

Analysing Coloured Petri Nets by the Occurrence Graph Method

This paper provides an overview og the work done for the author's PhD thesis. The research area of Coloured Petri Nets is introduced, and the available analysis methods are presented. The occurrence graph method, which is the main subject of this thesis, is described in more detail. Summaries of the six papers which, together with this overview, comprise the thesis are given, and the contributions are discussed.A large portion of this overview is dedicated to a description of related work. The aim is twofold: First, to survey pertinent results within the research areas of -- in increasing generality -- Coloured Petri Nets, High-level Petri Nets, and formalisms for modelling and analysis of parallel and distributed systems. Second, to put the results obtained in this thesis in a wider perspective by comparing them with important related work

Performance analysis and optimization of asynchronous circuits

Journal ArticleAsynchronous/Self-timed circuits are beginning to attract renewed attention as promising means of dealing with the complexity of modern VLSI designs. However, there are very few analysis techniques or tools available for estimating the performance of asynchronous circuits. In this paper we adapt the theory of Generalized Timed Petri-nets (GTPN) for analyzing and comparing a wide variety of asynchronous circuits, ranging from purely control-oriented circuits such as cross-bar arbiters to large asynchronous systems with data dependent control such as asynchronous processors. Experiments with the GTPN analyzer are found to track the observed performance of actual asynchronous circuits, thereby offering empirical evidence towards the soundness of the modeling approach. Our main contribution is in demonstrating how a quantitative design methodology for asynchronous circuits can be developed based on Timed Petri-nets

Analysis of Petri Net Models through Stochastic Differential Equations

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is not sufficiently high. Important phenomena that cannot be revealed include non-negligible variance and bi-modal population distributions. A less-known approximation proposed by Kurtz applies stochastic differential equations (SDEs) and provides information about the stochastic nature of the process. In this paper we apply and extend this diffusion approximation to study stochastic Petri nets. We identify a class of nets whose underlying stochastic process is a density dependent Markov chain whose indexing parameter is a multiplicative constant which identifies the population level expressed by the initial marking and we provide means to automatically construct the associated set of SDEs. Since the diffusion approximation of Kurtz considers the process only up to the time when it first exits an open interval, we extend the approximation by a machinery that mimics the behavior of the Markov chain at the boundary and allows thus to apply the approach to a wider set of problems. The resulting process is of the jump-diffusion type. We illustrate by examples that the jump-diffusion approximation which extends to bounded domains can be much more informative than that based on ODEs as it can provide accurate quantity distributions even when they are multi-modal and even for relatively small population levels. Moreover, we show that the method is faster than simulating the original Markov chain

EnPAC: Petri Net Model Checking for Linear Temporal Logic

State generation and exploration (counterexample search) are two cores of explicit-state Petri net model checking for linear temporal logic (LTL). Traditional state generation updates a structure to reduce the computation of all transitions and frequently encodes/decodes to read each encoded state. We present the optimized calculation of enabled transitions on demand by dynamic fireset to avoid such a structure. And we propose direct read/write (DRW) operation on encoded markings without decoding and re-encoding to make state generation faster and reduce memory consumption. To search counterexamples more quickly under an on-the-fly framework, we add heuristic information to the Buchi automaton to guide the exploration in the direction of accepted states. The above strategies can optimize existing methods for LTL model checking. We implement these optimization strategies in a Petri net model-checking tool called EnPAC (Enhanced Petri-net Analyser and Checker) for linear temporal logic. Then, we evaluate it on the benchmarks of MCC (Model Checking Contest), which shows a drastic improvement over the existing methods.Comment: 11 pages, 5 figure

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

More Efficient On-the-Fly Verification Methods of Colored Petri Nets

Colored Petri Nets (CP-nets or CPNs) are powerful modeling language for concurrent systems. As for CPNs' model checking, the mainstream method is unfolding that transforms a CPN into an equivalent P/T net. However the equivalent P/T net tends to be too enormous to be handled. As for checking CPN models without unfolding, we present three practical on-the-fly verification methods which are all focused on how to make state space generation more efficient. The first one is a basic one, based on a standard state space generation algorithm, but its efficiency is low. The second one is an overall improvement of the first. The third one sacrifices some applicability for higher efficiency. We implemented the three algorithms and validated great efficiency of latter two algorithms through experimental results