Petri net

About: Petri net is a research topic. Over the lifetime, 25039 publications have been published within this topic receiving 406994 citations.

Complexity metrics for Workflow nets

Abstract: Process modeling languages such as EPCs, BPMN, flow charts, UML activity diagrams, Petri nets, etc., are used to model business processes and to configure process-aware information systems. It is known that users have problems understanding these diagrams. In fact, even process engineers and system analysts have difficulties in grasping the dynamics implied by a process model. Recent empirical studies show that people make numerous errors when modeling complex business processes, e.g., about 20% of the EPCs in the SAP reference model have design flaws resulting in potential deadlocks, livelocks, etc. It seems obvious that the complexity of the model contributes to design errors and a lack of understanding. It is not easy to measure complexity, however. This paper presents three complexity metrics that have been implemented in the process analysis tool ProM. The metrics are defined for a subclass of Petri nets named Workflow nets, but the results can easily be applied to other languages. To demonstrate the applicability of these metrics, we have applied our approach and tool to 262 relatively complex Protos models made in the context of various student projects. This allows us to validate and compare the different metrics. It turns out that our new metric focusing on the structuredness outperforms existing metrics.

A Concept of Hierarchical Petri Nets with Building Blocks

Abstract: This paper introduces a formal concept of hierarchical Petri nets with building blocks The hierarchy concept allows to handle the refinement of places and transitions even if they are adjacent The building blocks are introduced as slightly restricted hierarchical Petri nets with hierarchically structured interfaces The main purpose of the concept is to facilitate the modeling of large real-world systems, rather than using them for theoretical considerations This will form the foundation of an editor-simulator-tool with a direct manipulation interface for this type of nets

The reachability problem for Petri nets is not elementary

Abstract: Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack. At the heart of our proof is a novel gadget so called the factorial amplifier that, assuming availability of counters that are zero testable and bounded by k, guarantees to produce arbitrarily large pairs of values whose ratio is exactly the factorial of k. We also develop a novel construction that uses arbitrarily large pairs of values with ratio R to provide zero testable counters that are bounded by R. Repeatedly composing the factorial amplifier with itself by means of the construction then enables us to compute in linear time Petri nets that simulate Minsky machines whose counters are bounded by a tower of exponentials, which yields the non-elementary lower bound. By refining this scheme further, we in fact establish hardness for h-exponential space already for Petri nets with h + 13 counters.

Petri nets and Other Models of Concurrency – ICATPN 2007

Abstract: Invited Papers.- Petri Nets, Discrete Physics, and Distributed Quantum Computation.- Autonomous Distributed System and Its Realization by Multi Agent Nets.- Petri Nets Without Tokens.- Toward Specifications for Reconfigurable Component Systems.- Generating Petri Net State Spaces.- Full Papers.- Markov Decision Petri Net and Markov Decision Well-Formed Net Formalisms.- Comparison of the Expressiveness of Arc, Place and Transition Time Petri Nets.- Improving Static Variable Orders Via Invariants.- Independence of Net Transformations and Token Firing in Reconfigurable Place/Transition Systems.- From Many Places to Few: Automatic Abstraction Refinement for Petri Nets.- A Compositional Method for the Synthesis of Asynchronous Communication Mechanisms.- History-Dependent Petri Nets.- Complete Process Semantics for Inhibitor Nets.- Behaviour-Preserving Transition Insertions in Unfolding Prefixes.- Combining Decomposition and Unfolding for STG Synthesis.- Object Nets for Mobility.- Web Service Orchestration with Super-Dual Object Nets.- Synthesis of Elementary Net Systems with Context Arcs and Localities.- Nets with Tokens Which Carry Data.- Operating Guidelines for Finite-State Services.- Theory of Regions for the Synthesis of Inhibitor Nets from Scenarios.- Utilizing Fuzzy Petri Net for Choreography Based Semantic Web Services Discovery.- Formal Models for Multicast Traffic in Network on Chip Architectures with Compositional High-Level Petri Nets.- Name Creation vs. Replication in Petri Net Systems.- Modelling the Datagram Congestion Control Protocol's Connection Management and Synchronization Procedures.- The ComBack Method - Extending Hash Compaction with Backtracking.- Computing Minimal Elements of Upward-Closed Sets for Petri Nets.- Tool Papers.- ProM 4.0: Comprehensive Support for Real Process Analysis.- dmcG: A Distributed Symbolic Model Checker Based on GreatSPN.- Workcraft: A Static Data Flow Structure Editing, Visualisation and Analysis Tool.

Macro E-Nets for Representation of Parallel Systems

Abstract: An extension of Petri nets called evaluation nets (E-nets) has been developed for use in representation of computer systems. These lead to interpreted graphs for use in human communication and to machine-interpretable descriptions. They may be used as aids in development of simulations and planning of measurements for examining characteristics such as throughput, turnaround time, and utilization of resources. This paper reviews the five primitives used to form nets expressing logical interactions among tokens (or tasks) flowing through the net and system resources represented by the net. Inherent in the use of the primitives is the ability to express time delays associated with the flow of tokens through the network and the modification of attributes of these tokens. This paper extends previous work on evaluation nets through the use of macro nets that represent structures made up of the primitives, allowing compression of the net for easier understanding. The macro nets are ``open-ended'' in the sense that the user can develop new macros to suit the needs of a particular study. Evaluation nets can be used informally like flow charts or block diagrams, although they provide greater power of expression than either. They can also be used more formally to develop machine aids, e.g., for on-line editing of evaluation nets or for development of simulation programs. Some examples of evaluation nets are provided that model a CDC 6400 and the cooperation of n independent sequential processes.