Generalized Asynchronous Systems

The paper is devoted to a mathematical model of concurrency the special case of which is asynchronous system. Distributed asynchronous automata are introduced here. It is proved that the Petri nets and transition systems with independence can be considered like the distributed asynchronous automata. Time distributed asynchronous automata are defined in standard way by the map which assigns time intervals to events. It is proved that the time distributed asynchronous automata are generalized the time Petri nets and asynchronous systems.Comment: 8 page

Business process modeling using petri nets with clocks

Petri Nets are tools for the analysis and design of concurrent systems. There is a formal theory, which supports Petri Nets. We propose Petri Nets with Clocks which has a high expressive power in the concurrent and asynchronous process modeling and gives the possibility to model real time systems. The Petri Nets with Clocks are useful to model systems with temporal requirements via specification of clocks, using temporal invariants for the places and temporal conditions in the transitions. Also, we have developed an algorithm for the analysis of Petri Nets with Clocks. For the Business Processes Modeling, we propose to use Petri Nets with Clocks to formalize models, allowing to study the models through a quantitative and qualitative analysis. Petri Nets with Clocks includes additional temporal elements -clocks-, which are appropriate for the Business Processes Modeling and are not taken into consideration in the literature concerning the extensions of Petri Nets with time. Petri Nets with Clocks allows studying the structural properties of Business Processes Modeling. This study not only allows the simulation but also verifies formally the model. It is oriented to the verification and correction of errors in the modeling of the time variable en Business Processes.Eje: Ingeniería de softwareRed de Universidades con Carreras en Informática (RedUNCI

Business process modeling using petri nets with clocks

Petri Nets are tools for the analysis and design of concurrent systems. There is a formal theory, which supports Petri Nets. We propose Petri Nets with Clocks which has a high expressive power in the concurrent and asynchronous process modeling and gives the possibility to model real time systems. The Petri Nets with Clocks are useful to model systems with temporal requirements via specification of clocks, using temporal invariants for the places and temporal conditions in the transitions. Also, we have developed an algorithm for the analysis of Petri Nets with Clocks. For the Business Processes Modeling, we propose to use Petri Nets with Clocks to formalize models, allowing to study the models through a quantitative and qualitative analysis. Petri Nets with Clocks includes additional temporal elements -clocks-, which are appropriate for the Business Processes Modeling and are not taken into consideration in the literature concerning the extensions of Petri Nets with time. Petri Nets with Clocks allows studying the structural properties of Business Processes Modeling. This study not only allows the simulation but also verifies formally the model. It is oriented to the verification and correction of errors in the modeling of the time variable en Business Processes.Eje: Ingeniería de softwareRed de Universidades con Carreras en Informática (RedUNCI

Membrane Systems with Priority, Dissolution, Promoters and Inhibitors and Time Petri Nets

We continue the investigations on exploring the connection between membrane systems and time Petri nets already commenced in [4] by extending membrane systems with promoters/inhibitors, membrane dissolution and priority for rules compared to the simple symbol-object membrane system. By constructing the simulating Petri net, we retain one of the main characteristics of the Petri net model, namely, the firings of the transitions can take place in any order: we do not impose any additional stipulation on the transition sequences in order to obtain a Petri net model equivalent to the general Turing machine. Instead, we substantially exploit the gain in computational strength obtained by the introduction of the timing feature for Petri nets

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

Educational process modelling with workflow and time Petri nets : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Computer Science at Massey University, Palmerston North, New Zealand

The research presented in this thesis describes how to use workflow management technology to model educational processes with a time axis. As workflow management technology has been widely used in modelling business processes, it has the potential to model educational processes. Based upon the components of workflow, educational processes and business processes have many common features such that educational processes can be modelled with workflow management technology. In addition, owing to the importance of the time component in processes, time Petri nets have been chosen as the design language for the modelling of the educational processes. The notation of time Petri nets has been illustrated in this thesis for the educational process. In this thesis, three different educational processes have been presented and modelled with workflow management technology as well as with time Petri nets individually. Furthermore, the architecture of the educational process management system has been constructed by adopting the reference model from the Workflow Management Coalition. To show the validity of using workflow management technology in the education domain, a sub-process of an educational process has been modelled and developed with certain developing techniques. It provides the potential research direction for further research on the modelling of educational process with workflow technology associated with a time component

Reachability of Communicating Timed Processes

We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its set of local clocks; all clocks evolve at the same rate. Our main contribution is a complete characterization of decidable and undecidable communication topologies, for both discrete and dense time. We also obtain complexity results, by showing that communicating timed processes are at least as hard as Petri nets; in the discrete time, we also show equivalence with Petri nets. Our results follow from mutual topology-preserving reductions between timed automata and (untimed) counter automata.Comment: Extended versio

Reduction rules for reset workflow nets

When a workflow contains a large number of tasks and involves complex control flow dependencies, verification can take too much time or it may even be impossible. Reduction rules can be used to abstract from certain transitions and places in a large net and thus could cut down the size of the net used for verification. Petri nets have been proposed to model and analyse workflows and Petri nets reduction rules have been used for efficient verification of various properties of workflows, such as liveness and boundedness. Reset nets are Petri nets with reset arcs, which can remove tokens from places when a transition fires. The nature of reset arcs closely relates to the cancellation behaviour in workflows. As a result, reset nets have been proposed to formally represent workflows with cancellation behaviour, which is not easily modelled in ordinary Petri nets. Even though reduction rules exist for Petri nets, the nature of reset arcs could invalidate the transformation rules applicable to Petri nets. This motivated us to consider possible reduction rules for reset nets. In this paper, we propose a number of reduction rules for Reset Workflow Nets (RWF-nets) that are soundness preserving. These reduction rules are based on reduction rules available for Petri nets [19] and we present the necessary conditions under which these rules hold in the context of reset nets