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Showing papers on "Process architecture published in 2016"


Journal ArticleDOI
TL;DR: To compare the modeling power of different Petri net generators, the notion of observation equivalence is proposed and ALPNs are shown to be the class of bounded generators possessing the highest modeling power.
Abstract: Observation structures considered for Petri net generators usually assume that the firing of transitions may be observed through a static mask and that the marking of some places may be measurable. These observation structures, however, are rather limited, namely they do not cover all cases of practical interest where complex observations are possible. We consider in this paper more general ones, by correspondingly defining two new classes of Petri net generators: labeled Petri nets with outputs (LPNOs) and adaptive labeled Petri nets (ALPNs). To compare the modeling power of different Petri net generators, the notion of observation equivalence is proposed. ALPNs are shown to be the class of bounded generators possessing the highest modeling power. Looking for bridges between the different formalisms, we first present a general procedure to convert a bounded LPNO into an equivalent ALPN or even into an equivalent labeled Petri net (if any exists). Finally, we discuss the possibility of converting an unbounded LPNO into an equivalent ALPN.

67 citations


Journal ArticleDOI
01 Apr 2016
TL;DR: An adaptive Petri net (APN) is proposed to model a self-adaptive software system and is an extension of hybrid Petri nets by embedding a neural network algorithm into them at some special transitions.
Abstract: Traditional models unable to model adaptive software systems since they deal with fixed requirements only, but cannot handle the behaviors that change at runtime in response to environmental changes. In this paper, an adaptive Petri net (APN) is proposed to model a self-adaptive software system. It is an extension of hybrid Petri nets by embedding a neural network algorithm into them at some special transitions. The proposed net has the following advantages: 1) it can model a runtime environment; 2) the components in the model can collaborate to make adaption decisions while the system is running; and 3) the computation is done at the local component, while the adaption is for the whole system. We illustrate the proposed APN by modeling a manufacturing system.

61 citations


Journal ArticleDOI
TL;DR: By modeling AMSs as Petri nets, this work develops an innovative distributed approach, which can create a trajectory leading to a desired goal and is adaptable to different kinds of applications.
Abstract: Due to the competition for limited resources by many concurrent processes in large-scale automated manufacturing systems (AMSs), one has to resolve any deadlock issue in order to reach their production goals without disruption and downtime. Monolithic resolution is a conventional approach for optimal or acceptable solutions, but may suffer from computational difficulty. Some decentralized methods are more efficient in finding approximate solutions, but most are application dependent. By modeling AMSs as Petri nets, we develop an innovative distributed approach, which can create a trajectory leading to a desired goal and is adaptable to different kinds of applications. Control strategies are applied to processes locally such that they can proceed concurrently and efficiently. Global goals are always reachable through the local observation, control, and execution of processes without knowing external and extra information. Polynomially complex are designed to find distributed controllers.

53 citations


Journal ArticleDOI
Guanjun Liu1
TL;DR: This paper defines a very general class of Petri nets called Petri Nets of Resource Allocation (PNRA) to model as many RASs as possible and proves that for the well-known G-system as a subclass of PNRAs, the deadlock problem is NP-complete.

50 citations


Journal ArticleDOI
TL;DR: This paper is motivated by FMSs' control; however, it is also applicable to other systems with discrete event controllers and some new theoretical results are developed.
Abstract: Modern complex systems require intensive application of sophisticated supervisors Structural simplification techniques are one of the fundamental researches in the context of flexible manufacturing systems (FMSs) They can reduce implementation cost, mitigate fabrication complexity, and improve reliability Several typical methods have been developed along this direction In order to thoroughly explore their effectiveness and performance, we not only conduct a comparison investigation but also develop some new theoretical results Several analytical results and performance measures are proposed for their qualitative and quantitative comparison Our approach can assist researchers and practitioners to better comprehend the inherent mechanisms and relative merits of these simplification methodologies as well as their applicability in FMSs This paper is motivated by FMSs’ control; however, it is also applicable to other systems with discrete event controllers

43 citations


Journal ArticleDOI
TL;DR: This paper proposes an algorithm to generate a finite prefix of the unfolding of a WF-net, called basic unfolding, and a necessary and sufficient condition is proposed to decide soundness based on basic unfolding.
Abstract: Workflow nets (WF-nets) as a class of Petri nets are widely used to model and analyze workflow systems. Soundness is an important property of WF-nets, which guarantees that the systems are deadlock- and livelock-free and each task has a chance to be performed. Van der Aalst has proven that the soundness problem is decidable for WF-nets and we have also shown that it is PSPACE-complete for bounded ones. Since the definition of soundness is based on reachability and Van der Aalst has proven that a sound WF-net must be bounded, the soundness detection can be carried out via the reachability graph analysis. However, the state explosion problem is a big obstacle to this technique. The unfolding technique of Petri nets can effectively avoid/alleviate this problem. This paper proposes an algorithm to generate a finite prefix of the unfolding of a WF-net, called basic unfolding . Furthermore, a necessary and sufficient condition is proposed to decide soundness based on basic unfolding. In addition, some examples illustrate that the unfolding technique can save the storage space effectively.

39 citations


Journal ArticleDOI
TL;DR: Algorithms with polynomial complexity are presented to find the optimal cycle time and the one-unit periodic schedule of a complex multi-cluster tool whose bottleneck individual tool is process-bound.
Abstract: Complex multi-cluster tools have been extensively used in semiconductor manufacturing. It is crucial to increase their productivity by their effective operation. With structural complexity, multiple robots, and the interaction among individual tools, it is very challenging to schedule a tree-like multi-cluster tool. This paper investigates the scheduling problem of such a tool whose bottleneck individual tool is process-bound. The system is modeled by well-known discrete-event models, i.e., resource-oriented Petri nets. Based on the models, for the first time, this work develops necessary and sufficient conditions under which a one-unit (wafer) periodic schedule exists and shows that an optimal one-unit periodic schedule can always be found. Algorithms with polynomial complexity are presented to find the optimal cycle time and the one-unit periodic schedule. Industrial examples are used to illustrate the proposed method, and they show that a significant reduction in cycle time can be obtained in comparison with the existing method.

38 citations


Journal ArticleDOI
TL;DR: A control architecture for reconfigurable manufacturing systems and its design method based on Petri nets, Service-Oriented Architecture and Holonic and Multi-Agent System techniques, among other good practices are proposed.

33 citations


Journal ArticleDOI
01 Apr 2016
TL;DR: An ordered weighted linguistic reasoning algorithm for knowledge representation and reasoning (OWLR) is developed and can allow the rule-based expert systems modeled with LRPNs to execute knowledge reasoning in a more flexible and intelligent manner.
Abstract: This paper proposes a linguistic reasoning Petri net (LRPN) model and develops an ordered weighted linguistic reasoning (OWLR) algorithm for knowledge representation and reasoning. Linguistic production rules in the knowledge base of a decision support system are modeled by LRPNs, where the truth degrees of the propositions in the linguistic production rules and the certainty factors of the rules are represented by linguistic 2-tuples. Moreover, both local and global weights of knowledge rules are taken into account in the linguistic reasoning process. The developed OWLR algorithm can allow the rule-based expert systems modeled with LRPNs to execute knowledge reasoning in a more flexible and intelligent manner. Finally, a case study regarding production rescheduling is presented to show the effectiveness and benefits of the proposed LRPN model and the linguistic reasoning approach.

29 citations


Journal ArticleDOI
TL;DR: This article applies reconfigurable object nets (RONs) for the modelling, simulation and analysis of RMSs and proposes a formal method, where the reconfiguration process is specified explicitly as a graph transformation.
Abstract: In reconfigurable manufacturing systems RMSs, the structure of the system can be changed during its execution. This reconfiguration can be triggered by several motivations: a new requirement in the production process, avoiding some problems caused by machines breakdowns, etc. RMSs are characterised by their flexibility which guarantees productivity and efficiency. However, their design is more complicated and needs new techniques and paradigms. The use of high level Petri nets PNs offers the ability to design these systems and to analyse their properties. In this article, the authors apply reconfigurable object nets RONs for the modelling, simulation and analysis of RMSs. Indeed, a formal method is proposed, where the reconfiguration process is specified explicitly as a graph transformation, the simulation is realised using the RON-tool, and the analysis exploits the TINA-tool timed nets analyser tool.

28 citations


Journal ArticleDOI
TL;DR: Decidability and undecidability results are obtained via a translation to data-centric dynamic systems, a recently devised framework for the formal specification and verification of data-aware business processes working over full-fledged relational databases with constraints.
Abstract: Petri nets with name creation and management ($${ u}$$ź-PNs) have been recently introduced as an expressive model for dynamic (distributed) systems, whose dynamics are determined not only by how tokens flow in the system, but also by the pure names they carry. On the one hand, this extension makes the resulting nets strictly more expressive than P/T nets: they can be exploited to capture a plethora of interesting systems, such as distributed systems enriched with channels and name passing, service interaction with correlation mechanisms, and resource-constrained workflow nets that explicitly account for process instances. On the other hand, fundamental properties like coverability, termination and boundedness are decidable for $${ u}$$ź-PNs. In this work, we go one step beyond the verification of such general properties, and provide decidability and undecidability results of model checking $${ u}$$ź-PNs against variants of first-order $${\mu}$$μ-calculus, recently proposed in the area of data-aware process analysis. While this model checking problem is undecidable in the general case, decidability can be obtained by considering different forms of boundedness, which still give raise to an infinite-state transition system. We then ground our framework to tackle the problem of soundness checking over workflow nets enriched with explicit process instances and resources. Notably, our decidability results are obtained via a translation to data-centric dynamic systems, a recently devised framework for the formal specification and verification of data-aware business processes working over full-fledged relational databases with constraints. In this light, our results contribute to the cross-fertilization between the area of formal methods for concurrent systems and that of foundations of data-aware processes, which has not been extensively investigated so far.

Journal ArticleDOI
01 Mar 2016
TL;DR: The goal of this paper is to make the modeling and execution aspects of BPM location-aware, i.e. to govern and constrain control-flow and process behavior based on location-based constraints by proposing a Petri net modeling extension which is formalized by means of a mapping to colored Petri nets (CPNs).
Abstract: Business process management (BPM) has emerged as one of the abiding systematic management approaches in order to design, execute and govern organizational business processes. Traditionally, most attention within the BPM community has been given to studying control-flow aspects, without taking other contextual aspects into account. This paper contributes to the existing body of work by focusing on the particular context of geospatial information. We argue that explicitly taking this context into consideration in the modeling and execution of business processes can contribute to improve their effectiveness and efficiency. As such, the goal of this paper is to make the modeling and execution aspects of BPM location-aware, i.e. to govern and constrain control-flow and process behavior based on location-based constraints. We do so by proposing a Petri net modeling extension which is formalized by means of a mapping to colored Petri nets (CPNs). Our approach has been implemented using CPN Tools and a simulation extension was developed to support the execution of location-aware process models. We also illustrate the feasibility of coupling business process support systems with geographic information systems by means of an experimental case.

Journal ArticleDOI
TL;DR: A prioritized colored Petri net (PCPN) model for CEP is proposed and conducted, and a case study is presented, as well as a discussion on the benefits from using PCPN for modeling CEP-based systems.
Abstract: Complex event processing (CEP) is a technology that allows us to process and correlate large volumes of data by using event patterns, aiming at promptly detecting specific situations that could require special treatment The event types and event patterns for a particular application domain are implemented by using an event processing language (EPL) Although some current model-driven tools allow end users to easily define these patterns, which are then transformed automatically into a particular EPL, the generated code is syntactically but not semantically validated To deal with this problem, a prioritized colored Petri net (PCPN) model for CEP is proposed and conducted in this paper This well-known graphical formalism together with CPNTools makes possible the modeling, simulation, analysis, and semantic validation of complex event-based systems To illustrate this approach, a case study is presented, as well as a discussion on the benefits from using PCPN for modeling CEP-based systems

Journal ArticleDOI
TL;DR: This framework provides an all-in-one modeling, scheduling, and simulation tool for integrated and collaborative project management in the Animation and Videogame (A&V) industry.

Journal ArticleDOI
TL;DR: This paper shows how SPLs can be modelled in an incremental, modular fashion using Feature Nets, provides a Feature Nets variant that supports modelling dynamic SPLs, and proposes an analysis method for SPL modelled as Feature Nets.
Abstract: Software product lines (SPLs) are diverse systems that are developed using a dual engineering process: (a) family engineering defines the commonality and variability among all members of the SPL, and (b) application engineering derives specific products based on the common foundation combined with a variable selection of features. The number of derivable products in an SPL can thus be exponential in the number of features. This inherent complexity poses two main challenges when it comes to modelling: firstly, the formalism used for modelling SPLs needs to be modular and scalable. Secondly, it should ensure that all products behave correctly by providing the ability to analyse and verify complex models efficiently. In this paper, we propose to integrate an established modelling formalism (Petri nets) with the domain of software product line engineering. To this end, we extend Petri nets to Feature Nets. While Petri nets provide a framework for formally modelling and verifying single software systems, Feature Nets offer the same sort of benefits for software product lines. We show how SPLs can be modelled in an incremental, modular fashion using Feature Nets, provide a Feature Nets variant that supports modelling dynamic SPLs, and propose an analysis method for SPL modelled as Feature Nets. By facilitating the construction of a single model that includes the various behaviours exhibited by the products in an SPL, we make a significant step towards efficient and practical quality assurance methods for software product lines.

Journal ArticleDOI
Dmitry A. Zaitsev1
01 May 2016
TL;DR: It is shown that Sleptsov place-transition nets (that allow transition firing in multiple instances at a step) run fast by implementing multiplication and division operations in polynomial time, and Petri nets (PNs) implement the mentioned operations in exponential time.
Abstract: We show that Sleptsov place–transition nets (that allow transition firing in multiple instances at a step) run fast by implementing multiplication and division operations in polynomial time. In comparison, Petri nets (PNs) implement the mentioned operations in exponential time. Moreover, PNs are obtained as a special case of Sleptsov nets (SNs) using loops with places having unit marking attached to each transition. In addition, we develop basics of an SN programming technology including basic operations and program composition rules. We provide examples of programs written in SN language for encryption/decryption with the RSA algorithm, calculation of fuzzy logic functions, and parallel calculation of the solutions to Laplace equations. SN computers promise hyper-performance because of a concurrent programming style consisting of a concise graphical language and small granulation of parallel processes on the level of separate events.

Book ChapterDOI
11 Apr 2016
TL;DR: A new modeling formalism is proposed for the specification of cyber-physical systems, combining the functionality offered by Petri nets and synchronous data flows, offering support for the design of mixed systems containing linear control and signal processing operations along with event driven elements.
Abstract: This paper proposes a new modeling formalism for the specification of cyber-physical systems, combining the functionality offered by Petri nets and synchronous data flows. Petri nets have been traditionally used to model the behavior of reactive systems, whose state evolves depending on the interaction with external events. On the opposite, data-flow formalisms have been used predominantly to describe data-driven systems that produce output data through mathematical transformations applied to input signals. The proposed formalism covers both kinds of problems, offering support for the design of mixed systems containing linear control and signal processing operations along with event driven elements. Model composition using multiple components communicating through input and output signals and events, enable the implementation of distributed cyber-physical systems. The new formalism and the respective execution semantics are presented, with special attention to the bidirectional interaction between Petri net elements and data-flow nodes.

01 Jan 2016
TL;DR: Stochastic petri nets an introduction to the theory of stochastic Petri nets, where people cope with some malicious bugs inside their computer and end up in infectious downloads.
Abstract: Thank you very much for reading stochastic petri nets an introduction to the theory. Maybe you have knowledge that, people have look hundreds times for their favorite novels like this stochastic petri nets an introduction to the theory, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they cope with some malicious bugs inside their computer.

Book ChapterDOI
01 Jan 2016
TL;DR: This chapter presents Petri nets based challenges to security such as Intrusion Detection System, security policy design and analysis, and cryptography tool.
Abstract: This chapter gives an introduction of Petri nets, its applications and security challenges. Petri nets are a graphical and mathematical modeling tool available to many systems. Once a system is modeled as a Petri net, the behavior of the system can be simulated by using tokens on the Petri net. Petri nets’ abundant techniques can be used to solve many problems associated with the modeled system. This chapter gives formal definitions, properties and analysis methods of Petri nets, and gives several examples to illustrate some basic concepts and successful application areas of Petri nets. Then this chapter presents Petri nets based challenges to security such as Intrusion Detection System, security policy design and analysis, and cryptography tool.

Proceedings ArticleDOI
04 Apr 2016
TL;DR: This work presents a novel approach for generating process models with structural properties that induce visually friendly layouts, rather than generating a single model that captures all behaviors, a set of Petri net models is delivered, each one covering a subset of traces of the log.
Abstract: Visualization is essential for understanding the models obtained by process mining. Clear and efficient visual representations make the embedded information more accessible and analyzable. This work presents a novel approach for generating process models with structural properties that induce visually friendly layouts. Rather than generating a single model that captures all behaviors, a set of Petri net models is delivered, each one covering a subset of traces of the log. The models are mined by extracting slices of labelled transition systems with specific properties from the complete state space produced by the process logs. In most cases, few Petri nets are sufficient to cover a significant part of the behavior produced by the log.

Journal ArticleDOI
TL;DR: In this paper, a timed colored Petri net with imposed time-space coupling safety constraints (TCCP-NET) is proposed to model and analyze integrated modular avionics (IMA), a real-time, safety-critical system.

Journal ArticleDOI
01 Jan 2016
TL;DR: First-order hybrid Petri nets can be efficiently used to model and manage intermodal freight transport terminals by enabling the terminal decision maker to choose the speeds associated with continuous transitions in order to optimize the terminal performance by two alternative control policies.
Abstract: In this paper, we show how first-order hybrid Petri nets can be efficiently used to model and manage intermodal freight transport terminals. The proposed formalism enables the terminal decision maker to choose the speeds associated with continuous transitions in order to optimize the terminal performance by two alternative control policies: the container flows maximization and the minimization of the residual containers in the storage area. The approach may be used either offline, to take decisions on the terminal resources, or online, to solve congestions/malfunctions. A real case study is modeled and managed by the proposed optimal control policies.

Journal ArticleDOI
TL;DR: The purpose of this paper is to combine Colored Petri Nets (CPNs) with an agent-based warehouse control system in order to model the system, evaluate petri net related system properties, and evaluate system performance.
Abstract: High accuracy modeling plays an important role for the optimization of planning and control in the supply chain members. Agent-based planning and control systems are efficient in representing intelligent manufacturing systems to achieve decision robustness. The purpose of this paper is to combine Colored Petri Nets CPNs with an agent-based warehouse control system in order to model the system, evaluate petri net related system properties, and evaluate system performance. A dynamic resource allocation of an order-picking process is presented as a case study to illustrate the applicability of the method. A hierarchical timed CPN CTPN model has been implemented. Simulation and state space results are used to identify system properties and evaluate performance.

Journal ArticleDOI
TL;DR: Novel techniques and a toolset are presented for automatically testing the conformance of software implementations against partial behavioral models constituted by a set of parameterized UML sequence diagrams, describing both external interactions with users or client applications and internal interactions between objects in the system.
Abstract: Novel techniques and a toolset are presented for automatically testing the conformance of software implementations against partial behavioral models constituted by a set of parameterized UML sequence diagrams, describing both external interactions with users or client applications and internal interactions between objects in the system. Test code is automatically generated from the sequence diagrams and executed on the implementation under test, and test results and coverage information are presented back visually in the model. A runtime test library handles internal interaction checking, test stubs, and user interaction testing, taking advantage of aspect-oriented programming techniques. Incremental conformance checking is achieved by first translating sequence diagrams to Extended Petri Nets that combine the characteristics of Colored Petri Nets and Event-Driven Petri Nets.

Journal ArticleDOI
TL;DR: This paper presents a first investigation of the synchronizing problem on unbounded systems, using synchronized Petri nets, i.e., nets whose evolution is driven by external input events, and shows that synchronizing sequences may be computed for a particular class of unbounded synchronizedPetri nets.
Abstract: Determining the state of a system when one does not know its current initial state is a very important problem in many practical applications as checking communication protocols, part orienteers, digital circuit reset, etc. Synchronizing sequences have been proposed in the 60's to solve the problem on systems modeled by finite state machines. This paper presents a first investigation of the synchronizing problem on unbounded systems, using synchronized Petri nets, i.e., nets whose evolution is driven by external input events. The proposed approach suffers from the fact that no finite space representation can exhaustively answer to the reachability problem but we show that synchronizing sequences may be computed for a particular class of unbounded synchronized Petri nets.

Book ChapterDOI
19 Oct 2016
TL;DR: The proposed approach is easy to implement and can be used as an effective production plans verification tool, to identify problems during the implementation of the control rules on production resources in the form of deadlocks, failure to disclose a bottleneck, or problems with production flow synchronization.
Abstract: In the paper, the problem of flow planning in production systems belonging to a class of Cyclic Concurrent Processes Systems is presented. The possibility of using Activity-oriented Petri Nets approach to model the problem as a discrete event system model, and then to perform simulations with the tool known as GPenSIM is shown. For simulation dispatching rules achieved by the analytical method of production order verification based on constraints sequencing methodology and its computer implementation in the system of production orders verification SWZ is used. This paper shows that the results achieved from GPenSIM agrees with that from SWZ. The proposed approach is easy to implement and can be used as an effective production plans verification tool, to identify problems during the implementation of the control rules on production resources in the form of deadlocks, failure to disclose a bottleneck, or problems with production flow synchronization.

Journal ArticleDOI
TL;DR: A bottom-up algorithm to transform a given generalized mutual exclusion constraint into an optimal admissible one and a design method is proposed to synthesize an optimal supervisor with polynomial complexity.

Proceedings ArticleDOI
27 May 2016
TL;DR: This paper regards an IoT service as a multi-agent system, and model it as an agent-oriented Petri net, called Petri nets in a PetriNet (PN2 for short) using the PN2 model, and analyzes the IoT service by simulation and model checking.
Abstract: In this paper, we proposed a system for analysis of IoT services. We regard an IoT service as a multi-agent system, and model it as an agent-oriented Petri net, called Petri nets in a Petri net (PN2 for short). Using the PN2 model, we analyze the IoT service by simulation and model checking. We also implemented the proposed system, and illustrated its usefulness with an application example for smart house.

Proceedings ArticleDOI
01 Nov 2016
TL;DR: The overall model consists of two interconnected Petri nets that represent, respectively, the physical part of the network (stations, blocks, crossovers, tracks, and so on, as well as trains travelling on the network) and the logical part of it (train schedule over the available lines).
Abstract: Petri nets and railway networks are considered in this paper with the aim of providing a comprehensive model to be used for analysis, optimisation, and control purposes. The overall model consists of two interconnected Petri nets that represent, respectively, the physical part of the network (stations, blocks, crossovers, tracks, and so on, as well as trains travelling on the network) and the logical part of it (train schedule over the available lines). The former Petri net has a fixed structure whereas the second one changes in accordance with the number of trains, lines, and timetable. In the paper, the main elements of the two Petri nets are described in detail, making use of an example of network which is representative of real-word railways. Moreover, some applications of the proposed model are discussed in order to highlight the effectiveness in employing Petri nets to analyse, optimise, and control railway networks and train schedules.

Journal ArticleDOI
TL;DR: This paper shows that both the SAT and CLP methods are overall faster by one or two orders of magnitude compared to the state-of-the-art algorithm from the Petri net community, and are in fact able to solve all the enumeration problems of the practical benchmarks.
Abstract: Petri nets are a simple formalism for modeling concurrent computation. They are also an interesting tool for modeling and analysing biochemical reaction systems, bridging the gap between purely qualitative and quantitative models. Biological networks can indeed be complex, large, and with many unknown kinetic parameters, which makes the development of quantitative models difficult. In this paper, we focus on the Petri net representation of biochemical reactions and on two structural properties of Petri nets, siphons and traps, that bring us information about the persistence of some molecular species, independently of the kinetics. We first study the theoretical time complexity of minimal siphon decision problems in general Petri nets, and present three new complexity results: first, we show that the existence of a siphon of a given cardinality is NP-complete; second, we prove that deciding the Siphon-Trap property is co-NP-complete; third, we prove that deciding the existence of a minimal siphon containing a given set of places, deciding the existence of a siphon of a given cardinality and deciding the Siphon-Trap property can be done in linear time in Petri nets of bounded tree-width. Then, we present a Boolean model of siphons and traps, and two method for enumerating all minimal siphons and traps of a Petri net, by using a SAT solver and a Constraint Logic Program (CLP) respectively. On a benchmark of 345 Petri nets of hundreds of places and transitions, extracted from biological models from the BioModels repository, as well as on a benchmark composed of 80 Petri nets from the Petriweb database of industrial processes, we show that both the SAT and CLP methods are overall faster by one or two orders of magnitude compared to the state-of-the-art algorithm from the Petri net community, and are in fact able to solve all the enumeration problems of our practical benchmarks. We investigate why these programs perform so well in practice, and provide some elements of explanation related to our theoretical complexity results.