Asymmetric Choice Nets Research Articles

Modular Reversibility Analysis in Self-loops Connections of Petri Net Systems

It is well known that the use of a modular approach for modeling has many advantages: it allows the modeler to consider different parts of the model independently of one another. A modular approach to analysis is also attractive: it often dramatically decreases the complexity of the analysis task. To create Petri net models of large systems, four bottom-up techniques, consisting of sharing operation, synchronous operation, self-loops connection as well as inhibitor-arc connection, have been developed. This paper focus on the concurrent behavior relation in self-loops connections of Petri net systems. First, for the property of dynamic invariance we show that it is possible to decide dynamic invariance of the global system from invariance of the individual modules. Second, for reversibility property we show that it is possible to construct reversibility of total modular system from reversibility of the individual modules without unfolding to the entire state space. Finally, we present some examples to illustrate the effectiveness of our approaches. The advantages of our approaches are in the context of concurrent language and can synthesize Petri net systems beyond asymmetric choice nets.

Property Analysis of Synthesis of Petri Nets Shared PP-Type Subnets

Petri net synthesis can avoid the state exploration problem, which is of exponential complexity, by guaranteeing the correctness in the Petri net while incrementally expanding the net. To solve the resource-sharing problem, Jiao L, et al., investigate the transformation of merging a set of places of an asymmetric choice (AC) net satisfying siphon-trap-property (ST-property), and present the conditions for it to preserve liveness, boundedness and reversibility. The major motivation of this paper is to generalize the results of Jiao’s research and to extend the place-merging problem to subnet-sharing synthesis problem on AC nets or Petri nets beyond AC nets. The conditions of liveness preservation, boundedness preservation and reversibility preservation are presented. The conditions are also presented to show that the synthesis net of AC nets is an AC net. These results are useful for studying the static and dynamic properties of Petri synthesis nets, and for analyzing properties of large complex system.

Maximal Class of Weakly Live Ordinary Petri Nets Without Emptiable Siphons

It is known that a net is deadlock free, not necessarily live, if no siphons can become empty. The key structure in making some transitions not live is called virtual first-order structure (VFOS). A net with (without) VFOS is called a virtual net (V net) [nonvirtual net (NV net)]. The V net is a maximal class of nets that may be weakly live and not live, if no siphons can become empty. Any net in the NV nets is live if and only if no siphons can become empty. In this paper, it is shown that asymmetric choice nets, synchronized choice nets, and extended synchronized choice nets belong to the NV nets.

Characterizing Liveness Monotonicity for Weighted Petri Nets in Terms of Siphon-Based Properties

A Petri net (N, M0) is monotonically live (m-live) if it remains live when the values of its initial marking M0 are increased. N is structurally m-live if there exists an initial marking M0 such that (N, M0) is m-live. Three new siphon-based characterizations for these properties are obtained: (1) For a weighted net N, the ST-property (i.e., every siphon contains a trap) is a necessary but not sufficient condition for N to be structurally m-live. (2) For a weighted net N, a necessary but not sufficient condition for (N, M0) to be m-live is that every siphon of N contains an M0-controlled trap (i.e., for every reachable marking M, the trap contains a place whose token value is not smaller than the least weight of its outgoing arcs). (3) A homogeneous asymmetric choice net (N, M0) is m-live if and only if every minimal siphon of N contains an M0-controlled trap. Characterization (3) is a generalization of Commoner's Theorem from ordinary liveness for ordinary free choice nets to m-liveness for homogeneous asymmetric choice nets.

On liveness and boundedness of asymmetric choice nets

This paper concerns two important techniques, characterization and property-preserving transformation, for verifying some basic properties of asymmetric choice Petri nets (AC nets). In the literature, a majority of the characterizations are for ordinary free choice nets. This paper presents many extended (from free choice nets) and new characterizations for four properties: liveness with respect to an initial marking, liveness monotonicity with respect to an initial marking, well-formedness, liveness and boundedness with respect to an initial marking. The nets involved are extended to homogeneous free choice nets, ordinary AC nets and homogeneous AC nets. This paper also investigates the transformation of merging a set of places of an ordinary AC net and proposes the conditions for it to preserve the siphon-trap-property (ST-property), liveness, boundedness and reversibility. The results are then applied to the verification of resource-sharing systems. At present, the major approaches for solving this problem are based on state machines or marked graphs and are not based on property preservation. Our approach extends the scopes of the underlying nets to AC nets and the verification techniques. It is found that the ST-property plays a very important role in many of the results. Furthermore, mainly through examples, the importance of the assumptions in the proposed characterizations and transformation and the limitation on further extensions are pointed out.

Notes on liveness and boundedness of extended strong asymmetric choice nets II

In this paper, the Extended Strong Asymmetric Choice Nets II (ESACN II), a subclass of Asymmetric Choice Nets (ACN) including Extended Free Choice Nets (EFCN) and Strong Asymmetric Choice Nets II (SACN II), is presented. A necessary and sufficient condition for liveness of ESACN II is proposed. Moreover, a criterion is introduced, which is necessary and sufficient for judgement of liveness and boundedness of ESACN II. Meanwhile a polynomial time algorithm is given to decide liveness and boundedness for ESACN II.

Liveness, fairness, and recurrence in Petri nets

In Petri net theory, a transition is called live if from every reachable marking there starts a computation in which the transition occurs. Another important property of a transition is the recurrent occurrence of the transition in every computation. In that case, we call the transition recurrent. Though liveness and recurrence of a transition are similar in spirit, there is a big di erence: Liveness only requires the possibility of transition occurrences whereas recurrence requires transition occurrences in every computation. Obviously, recurrence implies liveness. In this paper, we will investigate the reverse direction of this implication. In particular, we will characterize a class of Petri nets for which liveness implies recurrence. Basically, this class is asymmetric choice nets [7, 9] which is often also called extended simple nets [8, 6]. Since we extend the class

Two theoretical and practical aspects of knitting technique: invariants and a new class of Petri net

We present two aspects of knitting technique, the structural properties (especially the P- and T-invariants), and the synchronized choice net (a new class of Petri net), that are of both theoretical importance and practical uses to the verification of structural correctness of a Petri net or to detect the structural problem of a Petri net. This work first proves that the ordinary Petri nets synthesized with knitting technique are structurally bounded, consistent, conservative and safe (when each home place holds one token) using the well-known linear algebra approach. It also provides a procedure for finding P- and T-invariants for Petri net synthesized using the knitting technique. We present examples for P-invariants and show that we can synthesize Petri nets more general than the "asymmetric-choice nets". The algorithm for finding P-invariants of ordinary Petri nets is extended to find the P-invariants for a general Petri net synthesized with knitting technique and the arc-ratio rules. We present a new class of Petri nets, called synchronized choice nets, which are the largest set of Petri nets that can be covered by both T-components and P-components. An algorithm is proposed to find its T-components and the P-components, respectively. The complexity of this algorithm is also presented. The theory of synchronized choice nets has the potential to simplify that for free choice nets.

Deadlock analysis of Petri nets using siphons and mathematical programming

This paper exploits the potential of siphons for the analysis of Petri nets, It generalizes the well-known Commoner condition and is based on the notion of potential deadlocks which are siphons that eventually become empty. A linear programming based sufficient condition under which a siphon is not a potential deadlock is obtained. Based on the new sufficient condition, a mathematical programming approach and a mixed-integer programming approach are proposed for checking general Petri nets and structurally bounded Petri nets respectively without explicitly generating siphons. Stronger results are obtained for asymmetric choice nets and augmented marked graphs. In particular, we show that an asymmetric choice net is live iff it is potential-deadlock-free and an augmented marked graph is live and reversible iff it is potential-deadlock-free.