Many researchers have used hypercube interconnection networks for their good properties to construct many parallel processing systems. However, as the number of processors increases, the probability of occurrences of faulty nodes also increases. Hence, for hypercube interconnection networks which have faulty nodes, several efficient dynamic routing algorithms have been proposed which allow each node to hold status information of its neighbor nodes. In this paper, we propose an improved version of the algorithm proposed by Chiu and Wu by introducing the notion of full reachability. A fully reachable node is a node that can reach all nonfaulty nodes which have Hamming distance l from the node via paths of length l. In addition, we further improve the algorithm by classifying the possibilities of detours with respect to each Hamming distance between current and target nodes. We propose an initialization procedure which makes use of an equivalent condition to perform this classification efficiently. Moreover, we conduct a simulation to measure the improvement ratio and to compare our algorithms with others. The simulation results show that the algorithms are effective when they are applied to low-dimensional hypercube interconnection networks.

In computer science, concepts of resource such as data consumption and of time such as execution time are very important. Logical systems which can treat them have been applied in that field. Linear logic has been called a resource conscious logic. The expressive power is enough to describe a dynamic change in process environments. However, linear logic is not enough to treat a dynamic change in environments with the passage of time since it does not include a concept of time directly. A typical example is the relation between linear logic and Petri nets. It is well known that the reachability problem for Petri nets is equivalent to the provability for the corresponding sequent of linear logic. But linear logic cannot naturally represent timed Petri nets which are extensions of ordinary Petri nets with respect to time concept. So we extend linear logic with respect to time concept in order to introduce a resource-conscious and time-dependent logical system, that is, temporal linear logic. This system has some temporal operators "" which means a resource usable only once at the next time, "" which means a resource usable only once at anytime, and a modal storage operator "!" which means a resource usable any times at anytime. We can show that the reachability problem for timed Petri nets is equivalent to the provability for the corresponding sequent of temporal linear logic. In this paper, we also represent the description of synchronous communication model by temporal linear logic. The expressive power of temporal linear logic will be applicable to various fields of computer science.

This paper proposes a model checking method for microcomputer programs. To deal with the state explosion problem, we adopt a compositional verification approach. Based on the proposed method, a microcomputer program for a real-life air-conditioner is verified. The program is large enough to cause state explosion. Among fourteen typical properties of the program, five properties are successfully verified by our method.

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.

Given two terms and their rewriting rules, an unreachability problem proves the non-existence of a reduction sequence from one term to another. This paper formalizes a method for solving unreachability problems by abstraction; i. e. , reducing an original concrete unreachability problem to a simpler abstract unreachability problem to prove the unreachability of the original concrete problem if the abstract unreachability is proved. The class of rewriting systems discussed in this paper is called β rewriting systems. The class of β rewriting systems includes very important systems such as semi-Thue systems and Petri Nets. Abstract rewriting systems are also a subclass of β rewriting systems. A β rewriting system is defined on axiomatically formulated base structures, called β structures, which are used to formalize the concepts of "contexts" and "replacement," which are common to many rewritten objects. Each domain underlying semi-Thue systems, Petri Nets, and other rewriting systems are formalized by a β structure. A concept of homomorphisms from a β structure (a concrete domain) to a β structure (an abstract domain) is introduced. A homomorphism theorem (Theorem1)is established for β rewriting systems, which states that concrete reachability implies abstract reachability. An unreachability theorem (Corollary1) is also proved for β rewriting systems. It is the contraposition of the homomorphism theorem, i. e. , it says that abstract unreachability implies concrete unreachability. The unreachability theorem is used to solve two unreachability problems: a coffee bean puzzle and a checker board puzzle.

Consider a random digraph G=(V,A), where |V|=n and an arc (u,v) is present in A with probability p(n) independent of the existence of the other arcs. We discuss the expected number of vertices reachable from a vertex, the expected size of the transitive closure of G and their related topics based on the properties of reachability, where the reachability from a vertex s to t is defined as the probability that s is reachable to t. Let γn,p(n) denote the reachability s to t (s) in the above random digraph G. (In case of s=t, it requires another definition. ) We first present a method of computing the exact value of γn,p(n) for given n and p(n). Since the computation of γn,p(n) by this method requires O(n3) time, we then derive simple upper and lower bounds γn,p(n)U and γn,p(n)L on γn,p(n), respectively, and in addition, we give an upper bound n,p(n) on γn,p(n)U, which is easier to analyze but is still rather accurate. Then, we discuss the asymptotic behavior of n,p(n) and show that, if p(n)=α/(n-1), limnn,p(n) converges to one of the solutions of the equation 1-x-e-α x=0. Furthermore, as for (n) and (n), which are upper bounds on the expected number of reachable vertices and the expected size of the transitive closure of G, resp. , it turns out that limn(n) =α/(1-α) if p(n)=α/(n-1) for 0<α<1; otherwise either 0 or , and limn(n)=α if p(n)=α/(n-1)2 for α0; otherwise either 0 or .

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.

Verification of responsive communication protocols is to determine whether they can recover to a normal state within a predetermined time, even when they enter an abnormal state due to any fault. In this paper, we propose a new verification method for responsive communication protocols using virtual system states, each of which represents several system states. Next, in order to evaluate the effectiveness of the new method, we develop a verification tool based on the proposed method. Then we apply the tool to a broadcasting protocol and measure several metrics on the tool. The experimental results show that (1) the number of system states, (2) the amount of memory used by the tool, and (3) the execution time of the tool, can be drastically reduced.

A requirement specification acquisition method combined with hypothesis-based reasoning and model reasoning is proposed for obtaining service specifications from the ambiguous and/or incomplete requirement specifications of communications services. Errors at an early stage of software development cost more to debug than those at a later stage. Specification acquisition is the most upstream development process. Nevertheless, the system support for specification acquisition is delayed compared with other development phases.' Users do not always have precise requirements. It is therefore inevitable that user requirements contain ambiguities, insufficiencies and even contradictions. Considering this, it is indispensable to support a specification completion method that derives service specifications from such problem requirements. This paper proposes a combined method to obtain consistent and complete specifications from such problem requirements. Communications service specifications can be described by specifying terminal behaviors which can be recognized from outside the communications system(s). Such specifications are described by a rule-based language. Requirement specifications usually have components that are ambiguous, incomplete, or even contradictory. They appear as rule description and/or missing rules. From such requirements, service specifications are obtained by using hypothesis-based reasoning on input requirements and existing service specifications. When existing specifications cannot be used to obtain complementary specifications, a communications service model is used to propose new rules. The proposed methods are implemented as a part of a communications software development system. The system enables non-experts in communications systems to define their own service specifications.

In this paper we present an efficient method to solve reachability problems for Petri nets based on genetic algorithms and a kind of random search which is called postpone search. Genetic algorithm is one of algorithms developed for solving several problems of optimization. We apply GAs and postpone search to approximately solving reachability problems. This approach can not determine exact solutions, however, from applicability points of view, does not directly face state space explosion problems and can extend class of Petri nets to deal with very large state space in reasonable time. First we describe how to represent reachability problems on each of GAs and postpone search. We suppose the existence of a nonnegative parickh vector which satisfies the necessary reachability condition. Possible firing sequences of transitions induced by the parickh vector is encoded on GAs. We also define fitness function to solve reachability problems. Reachability problems can be interpreted as an optimization ones on GAs. Next we introduce random reachability problems which are capable of handling state space and the number of firing sequences which enable to reach a target marking from an initial marking. State space and the number of firing sequences are considered as factors which effect on the hardness of reachability problems to solve with stochastic methods. Furthermore, by using those random reachability problems and well known dining philosophers problems as benchmark problems, we compare GAs' performance with the performance of postpone search. Finally we present empirical results that GAa is more useful method than postpone search for solving more harder reachability problems from the both points of view; reliability and efficiency.

Petri nets are widely recognized as a powerful model for discrete event systems. Petri nets have both graphical and mathematical features. Graphical feature provides an environment to design and to comprehend discrete event systems. Mathematical feature provides an analysis power for verifying several properties of such systems. Several analysis techniques have been proposed so far, such as a reachability (coverability) graph method, a matrix equation approach, reduction or decomposition techniques, a symbolic model method and an unfolding method. The unfolding method was introduced to avoid generating the reachability graph. Unfoldings are often used in the verification of asynchronous circuits. This paper focuses on an analysis of finite state systems, i.e., bounded nets, and discuss a reachability problem and a upper bound problem. Relations between these problems and an unfolding have been clarified to provide a novel method to resolve these problems.

Petri net is a graphical and mathematical modeling tool for discrete event systems. This paper treats analysis problems for Petri nets under the earliest firing rule. Under this firing rule, transitions must fire as soon as they are enabled. Marked Petri nets under the earliest firing rule are called earliest firing systems, for short. First, some relations in analysis problems between the earliest and the normal firing systems are discussed. These problems include deadlock freedom, boundedness, persistency and liveness. Then, relations among three types of reachability are considered from the viewpoint of the earliest firing rule. Since earliest firing systems can simulate register machines, they have equivalent modeling powers to Turing machines. It suggests, however, that most of the analysis problems of earliest firing systems with general net structures are undecidable. In this paper, net structures are restricted to a subclass called dissynchronous choice (DC) nets. It is shown that the reachability problem from an initial marking to dead markings (markings where no transition can fire) in earliest firing DC systems is equivalent to the usual reachability problem of the same systems under the normal firing rule. Then, the result is applied to reachability problems of controlled DC systems in which some transitions in the net have external control input places. It is shown that for systems where every transition in the net has an external control input place, one type of reachability problem is decidable. Lastly, the liveness problem of earliest firing DC systems is considered and it is shown that this problem is equivalent to that of the underlying DC system under the normal firing rule. It is also shown that this liveness problem is decidable.

This paper discusses how to derive message sequence charts (MSCs) from a set of state transition descriptions. Recently, MSC notation has received much attention in the communications software field because it graphically shows system global behavior, So MSC handling techniques are being widely studied. These studies have recommended the design a system by a set of formal MSCs in the early stages of development and then to convert them into state transition descriptions. However, it is difficult to apply those results to existing communications software products. This is because these systems are designed based on state transition descriptions and there are no formal MSCs for them. In this paper, we propose a method of deriving MSCs based on optimized reachability analysis. This method generates MCSs that avoid state explosion. A case study using Q.931 protocol shows the feasibility of this method.

As to the method of multi-layer testing, up to now, the testing system (called PROVES) which testes effectively each N-layer protocol implement of SUT (System Under Test) using the functions of derail-points located between N-layer and (N+1)-layer protocol implements in a test system has been proposed. The test logic programs, which are embedded in the derail-points of the test system, play an important role to realize the protocol error test sequences in the test system. Namely, they modify, add, or delete the correct protocol commands/responses output from the protocol implement part of the lest system, sends these erroneous commands/responses to SUT and observes the output from SUT. This paper proposes the method of validating the correctness of test logic program using the structural properties of Petri nets without coding the test logic programs, where correctness means that the desired output can be obtained by sending or receiving the commands/responses within a constant time under the initial conditions determined uniquely by the test system and SUT. According to our experiment, it is seen that almost all of the logical errors included in the test logic programs used for the experiment can be detected by this method.

Until now, in a communication system which deals with multiple processes, system behavior has been described by a fixed number of processes. The state reachability problem for specified processes was generally deliberated within a pre-defined number of processes, and was analyzed by essentially searching for all possible behaviors. However, in a system whose number of processes is arbitrary, a given state which is not reachable in some situations which consists of a small number of processes might be reachable in another situation which consists of a larger number of processes. This article discusses the above problem, assuming that the behavior of a system is described by an arbitrary number of processes. After discussing the relationship between our model and the Petri net model, we clarify the properties between the set of reachable states and the number of processes involved in the system, and show an algorithm to obtain a sufficient number of processes for resolving the reachability problem.

In this paper, we propose an extended LR parsing algorithm, called LR parsing with a category reachability test (the LR-CRT algorithm). The LR-CRT algorithm enables a parser to efficiently recognize those sentences that belong to a specified grammatical category. The key point of the algorithm is to use an augmented LR parsing table in which each action entry contains a set of reachable categories. When executing a shift or reduce action, the parser checks whether the action can reach a given category using the augmented table. We apply the LR-CRT algorithm to improve a speech recognition system based on two-level LR parsing. This system uses two kinds of grammars, inter- and intra-phrase grammars, to recognize Japanese sentential speech. Two-level LR parsing guides the search of speech recognition through two-level symbol prediction, phrase category prediction and phone prediction, based on these grammars. The LR-CRT algorithm makes possible the efficient phone prediction based on the phrase category prediction. The system was evaluated using sentential speech data uttered phrase by phrase, and attained a word accuracy of 97.5% and a sentence accuracy of 91.2%

This paper proposes a test case generation method for testing concurrent programs as a black box. Typical applications are system testing for switching systems and inter-operability testing for OSI products. We adopt a two-step approach: first generate the control flow graph which represents global behaviors of a given concurrent program, and then apply conventional test case generation methods for the control flow graph. To generate a control flow graph without state space explosion, the black-box equivalence between system behaviors is introduced. The proposed algorithm generates a minimal control flow graph which consists of representatives of equivalence classes. Two practical techniques for the second step are discussed for a case study using a commercial digital PBX. The results show the feasibility of the proposed method.

Many practical communication protocols provide priority service as well as ordinary service. In such a protocol, the protocol machines can initiate a priority service at most of the states. This characteristic leads an extreme increment of the number of state transitions on the protocol machines and causes state space explosion in verification of safety property of the protocol. This paper describes a method of constructing a communication protocol from composition of a subprotocol for ordinary service and that for priority service. This paper also presents a sufficient condition for a composed protocol to inherit safety property from the subprotocols. By using the composition method and the sufficient condition, the decision problem for safety property of the composed protocol can be reduced to those of the subprotocols. An experimental result of verification of a part of OSI session protocol is also described. The result shows that the method can reduce the computation time for verifying safety property to about 3% against the naive way.