Analysis of Petri Nets and Transition Systems

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459

Petri net equivalence

Determining whether two Petri nets are equivalent is an interesting problem from both practical and theoretical standpoints. Although it is undecidable in the general case, for many interesting nets the equivalence problem is solvable. This paper explores, mostly from a theoretical point of view, some of the issues of Petri net equivalence, including both reachability sets and languages. Some new definitions of reachability set equivalence are described which allow the markings of some places to be treated identically or ignored, analogous to the Petri net languages in which multiple transitions may be labeled with the same symbol or with the empty string. The complexity of some decidable Petri net equivalence problems is analyzed

Analyzing safety and fault tolerance using time Petri nets

The application of time Petri net modelling and analysis techniques to safety-critical real-time systems is explored and procedures described which allow analysis of safety, recoverability, and fault tolerance. These procedures can be used to help determine software requirements, to guide the use of fault detection and recovery procedures, to determine conditions which require immediate miti gating action to prevent accidents, etc. Thus it is possible to establish important properties duing the synthesis of the system and software design instead of using guesswork and costly a posteriori analysis

Flat counter automata almost everywhere!

This paper argues that flatness appears as a central notion in the verification of counter automata. A counter automaton is called flat when its control graph can be ``replaced\u27\u27, equivalently w.r.t. reachability, by another one with no nested loops. From a practical view point, we show that flatness is a necessary and sufficient condition for termination of accelerated symbolic model checking, a generic semi-algorithmic technique implemented in successful tools like FAST, LASH or TReX. From a theoretical view point, we prove that many known semilinear subclasses of counter automata are flat: reversal bounded counter machines, lossy vector addition systems with states, reversible Petri nets, persistent and conflict-free Petri nets, etc. Hence, for these subclasses, the semilinear reachability set can be computed using a emph{uniform} accelerated symbolic procedure (whereas previous algorithms were specifically designed for each subclass)

Decidability Issues for Petri Nets

This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics

Synthesis of Bounded Choice-Free Petri Nets

This paper describes a synthesis algorithm tailored to the construction of choice-free Petri nets from finite persistent transition systems. With this goal in mind, a minimised set of simplified systems of linear inequalities is distilled from a general region-theoretic approach, leading to algorithmic improvements as well as to a partial characterisation of the class of persistent transition systems that have a choice-free Petri net realisation

On the decidability of fragments of the asynchronous π-calculus

AbstractWe study the decidability of a reachability problem for various fragments of the asynchronous π-calculus. We consider the combination of three main features: name generation, name mobility, and unbounded control. We show that the combination of name generation with either name mobility or unbounded control leads to an undecidable fragment. On the other hand, we prove that name generation without name mobility and with bounded control is decidable by reduction to the coverability problem for Petri Nets

Timed data flow diagrams

Traditional Data Flow Diagrams (DFD\u27s) are the cornerstone of the software development methodology known as Structured Analysis (SA), and they are probably the most widely used specification technique in industry today. DFD\u27s are popular because of their graphical representation and their hierarchical structure. Thus, they are well-suited for users with non-technical backgrounds and are commonly used to depict the static structure of information flow in a system. Numerous attempts to formalize DFD\u27s have appeared in the technical literature. We focus on the Formalized Data Flow Diagrams (FDFD\u27s) developed by Coleman, Wahls, Baker, and Leavens;This dissertation analyzes and extends FDFD\u27s with respect to their usefulness in specifying the qualitative and quantitative properties of real systems. Prior to this dissertation, there existed no well-founded knowledge about the computational power of FDFD\u27s nor any formal model in FDFD\u27s of the timing behavior of real systems;The dissertation is organized as a collection of five independent papers. Briefly, the main results of each paper are as follows: (i) Reduced FDFD\u27s are Turing equivalent. (ii) Stores, persistent flows, tests for empty flows, and infinite domains are not essential for FDFD\u27s. (iii) Subclasses of FDFD\u27s are equivalent to known subclasses of FIFO Petri Nets, immediately furnishing the decidability results for subclasses of FIFO Petri Nets to the corresponding subclasses of FDFD\u27s. (iv) A general stochastic model of time for FDFD\u27s (called Timed Data Flow Diagrams--TDFD\u27s) is defined, allowing not only a description of the relative likelihoods of various execution times, but also descriptions of the possible joint firing behavior of transitions. (v) An aggregation principle can be used for an efficient stochastic analysis of periodic TDFD\u27s with Markovian transition times;The results in this dissertation provide a firm theoretical foundation for further advances in Computer Science and Statistics, leading to practical and expressive tools for the specification and analysis of real systems