scholarly journals The Complexity of Synthesis of b-Bounded Petri Nets

2022 ◽  
Vol 183 (1-2) ◽  
pp. 125-167
Author(s):  
Ronny Tredup
Keyword(s):  
Petri Nets ◽  
Transition System ◽  
Decision Problems ◽  
Separation Property ◽  
Search Problem ◽  
Reachability Graph ◽  
System A ◽  
Fixed Type ◽  
Decision Version ◽  
State Separation

For a fixed type of Petri nets τ, τ-SYNTHESIS is the task of finding for a given transition system A a Petri net N of type τ(τ-net, for short) whose reachability graph is isomorphic to A if there is one. The decision version of this search problem is called τ-SOLVABILITY. If an input A allows a positive decision, then it is called τ-solvable and a sought net N τ-solves A. As a well known fact, A is τ-solvable if and only if it has the so-called τ-event state separation property (τ-ESSP, for short) and the τ-state separation property (τ-SSP, for short). The question whether A has the τ-ESSP or the τ-SSP defines also decision problems. In this paper, for all b ∈ ℕ, we completely characterize the computational complexity of τ-SOLVABILITY, τ-ESSP and τ-SSP for the types of pure b-bounded Place/Transition-nets, the b-bounded Place/Transitionnets and their corresponding ℤb+1-extensions.

AN OPERATIONAL SEMANTICS FOR THE PARALLEL LANGUAGE EDEN

2002 ◽  
Vol 12 (02) ◽  
pp. 211-228 ◽  
Author(s):  
MERCEDES HIDALGO-HERRERO ◽  
YOLANDA ORTEGA-MALLÉN
Keyword(s):  
Operational Semantics ◽  
Transition System ◽  
Lazy Evaluation ◽  
Parallel Language ◽  
Parallel Processes ◽  
System A ◽  
Independent Evaluation ◽  
Level Transition ◽  
Concurrent Algorithms ◽  
Main Thread

The functional parallel language Eden — suitable for the description of parallel and concurrent algorithms in a distributed setting — is an extension of Haskell with a set of coordination features. In this paper we present a formal operational semantics for the kernel of Eden, or more precisely, for a λ-calculus widened with explicit parallelism and potentially infinite communication channels. Eden overrides the lazy nature of Haskell on behalf of parallelism. This interplay between laziness and eagerness is accurately described by the semantics proposed here, which is based on Launchbury's natural semantics for lazy evaluation, and is expressed through a two-level transition system: a lower level for the local and independent evaluation of each process, and an upper one for the coordination between all the parallel processes in the system. As processes are created either under demand or in a speculative way, different scheduling strategies are possible — ranging from a minimal one that only allows the main thread to evolve, to a maximal one that evolves in parallel every active binding.

Algorithms of reduced complexity to design control sequences for untimed Petri nets in varying and uncertain environments

2018 ◽  
Vol 232 (6) ◽  
pp. 638-651
Author(s):  
Dimitri Lefebvre
Keyword(s):  
Petri Nets ◽  
Flexible Manufacturing ◽  
Manufacturing Systems ◽  
Discrete Event ◽  
Sufficient Conditions ◽  
Reference Value ◽  
Computational Effort ◽  
Scheduling Problems ◽  
Reachability Graph ◽  
Control Sequences

Petri nets have been widely used for the modelling, analysis, control and optimization of discrete event systems with shared resources in the domains of engineering. This article concerns the design of control sequences for such systems modelled with untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal size. Such sequences aim to move the marking from an initial value to a reference value. The resulting trajectory must avoid some forbidden markings and limit as possible the exploration of non-promising branches. For this purpose, the approach explores a small part of the reachability graph in the neighbourhood of the current marking. Then from the explored markings, it estimates a distance to the reference. The main contributions are (a) to reduce the explored part of the reachability graph according to a double limitation in breadth and in depth in order to provide solutions with a low computational effort; (b) to provide conditions to ensure the converge and optimality of the proposed algorithms and derive necessary and sufficient conditions for reachability; and (c) to include the firing sequence design in a global control schema suitable for reactive scheduling problems in uncertain and perturbed environments. The main application concerns deadlock-free scheduling problems in the domain of flexible manufacturing systems, but the approach is also applicable for systems in computer science and transportation.

Target-oriented Petri Net Synthesis

2020 ◽  
Author(s):  
Eike Best ◽  
Raymond Devillers ◽  
Evgeny Erofeev ◽  
Harro Wimmel
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Transition System ◽  
Efficient Synthesis ◽  
Transition Systems ◽  
Np Complete ◽  
Full Class ◽  
Petri Net Synthesis ◽  
Labelled Transition System ◽  
Additional Constraints

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

A New Deadlock Avoidance Policy Based on Petri Nets in Distributed System

2015 ◽  
Vol 743 ◽  
pp. 575-580
Author(s):  
B.W. Liu
Keyword(s):  
Petri Nets ◽  
Distributed System ◽  
Traditional Method ◽  
Deadlock Avoidance ◽  
Reachability Graph ◽  
Concurrent Process

Distributed system has the characteristic of high concurrency, which often leads to deadlock due to the execution of concurrent process. By applying Petri nets model can effectively solve this problem. In this paper, based on Petri nets model, we propose a new efficient deadlock avoidance policy for distributed system by using the Petri reachability graph. At last we analysis the different performance between this algorithm and the traditional method by using Matlab tool.

On near-optimal deadlock control for a class of generalized Petri nets using reachability graph

2017 ◽  
Vol 34 (6) ◽  
pp. 1896-1922
Author(s):  
YiFan Hou ◽  
Murat Uzam ◽  
Mi Zhao ◽  
ZhiWu Li
Keyword(s):  
Petri Nets ◽  
Flexible Manufacturing ◽  
Manufacturing Systems ◽  
Control Method ◽  
Optimal Solution ◽  
Iteration Step ◽  
Reachability Graph ◽  
Content Type ◽  
Multiple Resource ◽  
Invariant Control

Purpose Deadlock is a rather undesirable phenomenon and must be well solved in flexible manufacturing systems (FMS). This paper aims to propose a general iterative deadlock control method for a class of generalized Petri nets (GPN), namely, G-systems, which can model an FMS with assembly and disassembly operations of multiple resource acquisition. When given an uncontrolled G-system prone to deadlocks, the work focuses on the synthesis of a near-optimal, non-blocking supervisor based on reachability graph (RG) analysis. Design/methodology/approach The concept of a global idle place (GIP) for an original uncontrolled G-system is presented. To simplify the RG computation of an uncontrolled G-system, a GIP is added temporarily to the net model during monitor computation steps. Starting with one token and then by gradually increasing the number of tokens in the GIP at each iteration step, the related net system is obtained. The minimal-covered-set of all bad markings of the related net system suffering from deadlock can be identified and then removed by additional monitors through an established place-invariant control method. Consequently, all related systems are live, and the GIP is finally removed when the non-blockingness of the controlled system is achieved. Meanwhile, the redundancy of monitors is also checked. Findings A typical G-system example is provided to demonstrate the applicability and effectiveness of the proposed method. Experiments show that the proposed method is easy to use and provides very high behavioral permissiveness for G-system. Generally, it can achieve an optimal or a near-optimal solution of the non-blocking supervisor. Originality/value In this work, the concept of GIP for G-systems is presented for synthesis non-blocking supervisors based on RG analysis. By using GIP, an effective deadlock control method is proposed. Generally, the proposed method can achieve an optimal or a near-optimal, non-blocking supervisor for an uncontrolled G-system prone to deadlocks.

scholarly journals Computation of the Reachability Graph of untimed Hybrid Petri nets

1970 ◽  
Vol 1 ◽  
pp. 27-28
Author(s):  
Estibaliz Fraca ◽  
Jorge Júlvez ◽  
Manuel Silva
Keyword(s):  
Dynamical Systems ◽  
Petri Nets ◽  
Reachability Graph ◽  
Hybrid Petri Nets

Untimed hybrid Petri nets are a formalism for the analysis of dynamical systems, which combines discrete and continuous behaviour. The study of its reachability is interesting for analysis purposes, such as the study of behavioural properties. A method to compute its reachability graph and reachability space is proposed here.

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