A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Computing Optimal Coverability Costs in Priced Timed Petri Nets

We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Our cost model assigns token storage costs per time unit to places, and firing costs to transitions. We study the cost to reach a given control-state. In general, a cost-optimal run may not exist. However, we show that the infimum of the costs is computable.Comment: 26 pages. Contribution to LICS 201

A Petri net design, simulation, and verification tool

Increasing desire for thorough simulation and analysis of engineered products is quickly replacing the prototype and test design model. Petri nets are important instruments for modeling concurrent, distributed, asynchronous, parallel, deterministic, and non-deterministic systems. This tool provides designers with the ability to easily specify a Petri net design with an easy to use user interface, then simulate and analyze the Petri net to determine essential design properties using the reachability tree technique. The tool will construct a reachability tree, then analyze the tree for properties of safeness, boundedness, liveness, and conservativeness

Computer implementation of Mason\u27s rule and software development of stochastic petri nets

A symbolic performance analysis approach for discrete event systems can be formulated based on the integration of Petri nets and Moment Generating Function concepts [1-3]. The key steps in the method include modeling a system with arbitrary stochastic Petri nets (ASPN), generation of state machine Petri nets with transfer functions, derivation of equivalent transfer functions, and symbolic derivation of transfer functions to obtain the performance measures. Since Mason\u27s rule can be used to effectively derive the closed-form transfer function, its computer implementation plays a very important role in automating the above procedure. This thesis develops the computer implementation of Mason\u27s rule (CIMR). The algorithms and their complexity analysis are also given. Examples are used to illustrate CIMR method\u27s application for performance evaluation of ASPN and linear control systems. Finally, suggestions for future software development of ASPN are made

Software development for analysis of stochastic petri nets using transfer functions

This thesis research is an implementation of a closed-form analytical technique for study, evaluation and analysis of Stochastic Petri Nets (SPN). The technique is based on a theorem that an isomorphism exists between an SPN and a Markov Chain. The procedure comprises five main steps: reachability graph generation of the underlying Petri net, transformation of the reachability graph to a state machine Petri net, calculation of transfer functions, computation of equivalent transfer functions via Mason\u27s rule, and computation of performance parameters of the SPN model from the equivalent transfer functions and their derivatives. The software is developed in UNIX using C and applied to various SPN models. Future research includes implementation of Mason\u27s rule for complex cases and symbolic derivation of equivalent transfer functions

Complexity Hierarchies Beyond Elementary

We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep updating the catalogue of problems from Section 6 in future revision