This paper considers two simulation models for simple unreliable file systems with checkpointing and rollback recovery. In Model 1, the checkpoint is generated at a pre-specified time and the information on the main memory since the last checkpoint is back-uped in a secondary medium. On the other hand, in Model 2, the checkpointing is executed at the time when the number of transactions completed for processing is achieved at a pre-determined level. However, it is difficult to treat such models analytically without employing any approximation method, if queueing effects related with arrival and processing of transactions can not be ignored. We apply the generalized stochastic Petri net (GSPN) to represent the stochastic behaviour of systems under two checkpointing schemes. Throughout GSPN simulation, we evaluate quantitatively the maintainability of checkpoint models under consideration and examine the dependence of model parameters in the optimal checkpoint policies and their associated system availabilities.

The quality of an architectural design of a software system has a great influence on achieving non-functional requirements to the system, so formal evaluation and validation techniques to designed architectures are necessary in the early phase of development processes. In this paper, we present a technique for describing software architectures formally based on Coloured Petri Nets (CPNs) and a technique for reusing architectural constituents. Architectural descriptions are essentially written with a CPN language, so that the evaluation and analysis on the architectural descriptions can be made in architectural design phrase. We extract reusable architectural parts from standard architecture styles and architectural patterns so that a designer can construct an architecture by only retrieving the parts and combine them. We also designed the language for describing the combination of the architectural parts. To show the effectiveness of our techniques, we illustrate how a blackboard architecture can be composed of reusable parts and be simulated on a CPN tool (Design/CPN).

Software Composition is one of the major concerns in component based software development (CBSD). In this paper, we present a formal approach to construct software systems from requirements models using available components. We focus on the knowledge resides in the requirements and the components in order to deal with those heterogeneous concepts. This approach consists of three steps. The first step is selecting adaptable components to the requirements model. The requirements and the components are transformed into the form of Σ algebra, and the component adaptability is evaluated by Σ homomorphism. Rough Set Theory (RST) is used to make carriers of two Σ algebras common, which are derived from the requirements and the components. The second step is identifying the control structure of the requirements. Decision tables are used for representing the knowledge on the requirements, and RST is used to optimize the control structure. The third step is to implement the control structure as glue codes which would perform the components appropriately. This approach mainly focuses on enterprise back-office applications in this paper, however, it can be easily applied to other domains, since it assumes the requirements to be expressed in Colored Petri Nets (CPN), and CPN can express various problem domains other than enterprise back-office applications.

The subject of the paper is to give an overview and latest results on the Legal Firing Sequence Problem of Petri nets (LFS for short). LFS is very fundamental in the sense that it appears as a subproblem or a simpler form of various basic problems in Petri net theory, such as the well-known marking reachability problem, the minimum initial resource allocation problem, the liveness (of level 4) problem, the scheduling problem and so on. However, solving LFS generally is not easy: it is NP -hard even for Petri nets having very simple structures. This intractability of LFS may have been preventing us from producing efficient algorithms for those problems. So research on LFS from computational complexity point of view seems to be rewarding.

The legal firing sequence problem (LFS) asks if it is possible to fire each transition some prescribed number of times in a given Petri net. It is a fundamental problem in Petri net theory as it appears as a subproblem, or as a simplified version of marking reachability, minimum initial resource allocation, liveness, and some scheduling problems. It is also known to be NP-hard, however, even under various restrictions on nets (and on firing counts), and no efficient algorithm has been previously reported for any class of nets having general edge weights. We show in this paper that LFS can be solved in polynomial time (in O(n log n) time) for a subclass of state machines, called cacti, with arbitrary edge weights allowed (if each transition is asked to be fired exactly once).

Adaptability evaluation of software systems is one of the key concerns in both software engineering and requirements engineering. In this paper, we present a formal and systematic approach to evaluate adaptability of software systems to requirements in enterprise business applications. Our approach consists of three major parts, that is, the common modeling method for both business realms and software realms, functional adaptability evaluation between the models with Σ algebra and behavioral adaptability evaluation with process algebra. By our approach, one can rigorously and uniquely determine whether a software system is adaptable to the requirements, either totally or partially. A sample application from an order processing is illustrated to show how this approach is effective in solving the adaptability evolution problem.

Given a Petri net N=(P, T, E), a siphon is a set S of places such that the set of input transitions to S is included in the set of output transitions from S. Concerning extraction of one or more minimal siphons containing a given specified set Q of places, the paper shows several results on polynomial time solvability and NP-completeness, mainly for the case |Q| 1.

Petri net is an efficient model for concurrent systems. Liveness is one of analysis properties of Petri net. It concerns with potential fireability of transitions. Many studies have been done on liveness of Petri nets and subclasses are suggested with liveness criteria. In this paper, extended partially ordered condition (EPOC) net is suggested and its liveness is studied. Equivalence of liveness and place-liveness is derived. Analysis using siphon and traps are done. Liveness under the earliest firing rule, where transition must fire as soon as it is enabled, is also studied.

Given a Petri net PN=(P, T, E), a siphon is a set S of places such that the set of input transitions to S is included in the set of output transitions from S. Concerning extraction of minimal siphons containing a given specified set Q of places, the paper proposes three algorithms based on branch-and-bound method for enumerating, if any, all minimal siphons containing Q, as well as for extracting such one minimal siphon.

Petri net is a graphical and mathematical modeling tool for discrete event systems. This paper treats analysis problems of time Petri nets. In this model, a minimal and a maximal firing delays are assigned to each transition. If a transition is 'enabled' it can fire after minimal delay has passed and must fire before maximal delay has elapsed. Since time Petri net can simulate register machines, it has equivalent modeling power to that of Turing machine. It means, however, that most of the analysis problems of time Petri nets with general net structures are undecidable. In this paper, net structures are restricted to a subclass called partially ordered condition (POC) nets and dissynchronous choice (DC) nets. Firing delays are also restricted to satisfy 'static fair condition' which assures chance to fire for all transitions enabled simultaneously. First, a sufficient condition of liveness of time POC net with the static fair condition is derived. Then it is shown that liveness of time DC net with static fair condition is equivalent to liveness of the underlying nontime net. This means that liveness problem of this class is decidable. Lastly, liveness problem of extended free choice (EFC) net is shown to be decidable.

This paper presents a new approach to computer image generation via three proposed methods for translating the evolution of a Petri net into fractal image synthesis. The idea is derived from the concept of fractal iteration principles in the escape-time algorithm and chaos game. The approach uses a Petri net as a powerful abstract modeling tool for fractal image synthesis via its duality, deadlock, inhibitor arc, firing sequence and marking reachability. The objective of this approach is to enhance the analysis technique of a Petri net and use it as a novel technique for fractal image synthesis. Generating fractal images via the dynamics of a Petri net allows an easy and direct proof for the similarity and correspondence between the dynamics of complex quadratic fractals by the recursive procedure of the escape-time algorithm and the state of a Petri net via a reachability problem. The reachability problem will be manipulated in terms of the dynamics of the fractal in order to generate images via three proposed methods. Validation of our approach is given by discussion and an illustration of some experimental results.

This paper proposes an algorithm for analyzing the reachability property of Petri nets by the use of unfoldings. It is known that analyzing the reachability by using unfoldings requires exponential time and space to the size of unfolding. The algorithm is based on the branch and bound technique, and experimental results show efficiency of the algorithm.

In order to reduce state explosion problem, techniques such as symbolic state space traversal and partial order reduction have been proposed. Combining these two techniques, however, seems difficult, and only a few research projects related to this topic have been reported. In this paper, we propose handling single place zero reachability problem of Petri nets by using both partial order reduction and symbolic state space traversal based on ZBDDs. We also show experimental results of several examples.

In this paper, a new method is proposed for solving forbidden state problems in non-ordinary controlled Petri nets (NCPNs) with uncontrollable transitions. Using a precedence subnet and a boundary subnet with decision-free properties, the behavior of markings are analyzed structurally. An efficient algorithm is presented for calculating the number of total tokens in forbidden places reachable from a marking. This paper derives necessary and sufficient conditions for identifying admissible markings and boundary markings in terms of the precedence subnet and the boundary subnet.

In scheduling problem for automatic assembly, planning of task sequence is closely related with resource allocation. However, they have been separately carried out with little interaction in previous work. In assembly planning problem, there are many feasible sequences for one mechanical product. In order to find the best assembly sequence, we have to decide the cost function for each task a priori and make decision based on summation of costs in sequence. But the cost of each task depends on the machine which executes the allocated task and it becomes difficult to estimate an exact cost of each task at planning stage. Moreover, no concurrent operation is taken into account at planning stage. Therefore, we must consider the sequence planning and the machine allocation simultaneously. In this paper, we propose a new scheduling method in which sequence planning and machine allocation are considered simultaneously. First of all, we propose a modeling method for an assembly sequence including a manufacturing environment. Secondly, we show a guideline in order to determine the estimate function in A* algorithm for assembly scheduling. Thirdly, a new search method based on combination of A* algorithm and supervisor is proposed. Fourthly, we propose a new technique which can take into consider the repetitive process in manufacturing system so as to improve the calculation time. Finally, numerical experiments of proposed scheduling algorithm are shown and effectiveness of proposed algorithm is verified.

A formal necessary and sufficient condition on the general Petri net reachability problem is presented by eliminating all spurious solutions among known nonnegative integer solutions of state equation and unifying all the causes of those spurious solutions into a maximal-strongly-connected and siphon-and-trap subnet Nw. This result is based on the decomposition of a given net (N, Mo) with Md and the concepts of "no immature siphon at the reduced initial marking Mwo" and "no immature trap at the reduced end marking Mwd" on Nw which are both extended from "no token-free siphon at the initial marking Mo" and "no token-free trap at the end marking Md" on N, respectively, which have been both effectively, explicitly or implicitly, used in the well-known fundamental and simple subclasses.

Unfolding originally introduced by McMillan is gaining ground as a partial-order based method for the verification of concurrent systems without state space explosion. However, it can be exposed to redundancy which may increase its size exponentially. So far, there have been trials to reduce such redundancy resulting from conflicts by improving McMillan's cut-off criterion. In this paper, we show that concurrency is also another cause of redundancy in unfolding, and present an algorithm to reduce such redundancy in live, bounded and reversible Petri nets which is independent of any cut-off algorithm.

Basic structural characteristics, which are useful in modular synthesis based on strongly connected state machines, of SMA/LBFC nets are discussed in this paper. A more convincing and direct proof of the equivalence of two structural characterization of the class of Petri nets is given. This proof will give clearer view of the structural characteristics of LBFC/SMA nets. On the other hand, however, the structural characteristics are not practically amenable in application to modular synthesis of SMA nets from a given set of SCSM's since all possible SCSM's should be examined for the verification of the given conditions. The later half of this paper is devoted into strengthening the results, i. e. , in composition of an SMA net from a given set of SCSM's the condition is also satisfied in any SCSM generated by composition.

Silva et al. has suggested a criterion based on incidence matrix to verify if a given extended free choice net has a live and bounded marking. This paper shows that this criterion is a necessary and sufficient condition that a given net is a state machine allocatable (SMA) net. This result gives a polynomial algorithm to verify SMA net.

Geometric region method is one of the techniques to handle real-time systems which have potentially infinite state spaces. However, the original geometric region method gives incorrect results for the CTL model checking of time Petri nets. In this paper, we discuss the sufficient condition for the geometric region graphs to be correct with respect to the CTL model checking of time Petri nets, and then propose a technique to partition given geometric regions so that the graphs satisfy the sufficient condition. Finally, we implement the proposed algorithm, and compare it with the other methods by using small examples.