This paper presents a new method to translate a regular expression into a nondeterministic finite automaton (an NFA for short). Let r be a regular expression and let M be a Thompson automaton for r. We first introduce a labeled Thompson automaton defined by assigning two types of expressions which denote prefixes and suffixes of words in L(r) to each state of M. Then we give new ϵ-free NFAs constructed from a labeled Thompson automaton. These NFAs are called a prefix equation automaton and a suffix equation automaton. We show that a suffix equation automaton is isomorphic to an equation automaton defined by Antimirov. Furthermore we give an NFA called a unified equation automaton by joining two NFAs. Thus the number of states of a unified equation automaton can be smaller than that of an equation automaton.

We consider the bisimilarity control problem for partially observed nondeterministic discrete event systems with deterministic specifications. This problem requires us to synthesize a supervisor that achieves bisimulation equivalence of the supervised system and the deterministic specification under partial observation. We present necessary and sufficient conditions for the existence of such a deterministic supervisor and show that these conditions can be verified polynomially.

This paper investigates the closure properties of multi-inkdot nondeterministic Turing machines with sublogarithmic space. We show that the class of sets accepted by the Turing machines is not closed under concatenation with regular set, Kleene closure, length-preserving homomorphism, and intersection.

We consider a similarity control problem for discrete event systems modeled as nondeterministic automata. A nonblocking supervisor was synthesized in the previous work under the assumption that the event occurrence and the current state of the plant are observable. In this letter, we prove that the synthesized supervisor is a maximally permissive nonblocking one.

In this paper, we consider a similarity control problem for nondeterministic discrete event systems, which requires us to synthesize a nonblocking supervisor such that the supervised plant is simulated by a given specification. We assume that a supervisor can observe not only the event occurrence but also the current state of the plant. We present a necessary and sufficient condition for the existence of a nonblocking supervisor that solves the similarity control problem and show how to verify it in polynomial time. Moreover, when the existence condition of a nonblocking supervisor is satisfied, we synthesize such a supervisor as a solution to the similarity control problem.

We consider a decentralized similarity control problem for composite nondeterministic discrete event systems, where each subsystem has its own local specification and the entire specification is described as the synchronous composition of local specifications. We present necessary and sufficient conditions for the existence of a complete decentralized supervisor that solves a similarity control problem under the assumption that any locally uncontrollable event is not shared by other subsystems. We also show that the system controlled by the complete decentralized supervisor that consists of maximally permissive local supervisors is bisimilar to the one controlled by the maximally permissive monolithic supervisor under the same assumption.

In this paper, we consider a similarity control problem for plants and specifications, modeled as nondeterministic automata. This problem requires us to synthesize a nondeterministic supervisor such that the supervised plant is simulated by a given specification. We assume that a supervisor can observe not only the event occurrence but also the current state of the plant. First, we derive a necessary and sufficient condition for the existence of a complete supervisor, which is a solution to the similarity control problem. Then, we present a method for synthesizing a maximally permissive similarity enforcing supervisor when the existence condition is satisfied.

In this paper, we study a supervisory control problem for plants and specifications modeled by nondeterministic automata. This problem requires to synthesize a nondeterministic supervisor such that the supervised plant is bisimilar to a given specification. We assume that a supervisor can observe not only the event occurrence but also the current state of the plant, and introduce a notion of completeness of a supervisor which guarantees that all nondeterministic transitions caused by events enabled by the supervisor are defined in the supervised plant. We define a notion of partial bisimulation between a given specification and the plant, and prove that it serves as a necessary and sufficient condition for the existence of a bisimilarity enforcing complete supervisor.

This paper investigates the closure properties of 1-inkdot nondeterministic Turing machines and 1-inkdot alternating Turing machines with only universal states which have sublogarithmic space. We show for example that the classes of sets accepted by these Turing machines are not closed under length-preserving homomorphism, concatenation with regular set, Kleene closure, and complementation.

Recently, for more efficient filtering of XML data, YFilter system has been suggested to exploit the prefix commonalities that exist among path expressions. Sharing the prefix commonality gives the benefit of improving filtering performance through the tremendous reduction in filtering machine size. However, exploiting the postfix commonality can also be useful for an XML filtering situation. For example, when a stream of XML messages does not have any defined schema, or users cannot remember the defined schema exactly, users often use the partial matching path queries which begins with the descendant axis ("//"), e.g., '//science/article/title', '//entertainment/article/title', and '//title'. If so, the registered XPath queries are most likely to have the postfix commonality, e.g., the sample queries share the partial path expressions 'article/title' and 'title'. Therefore, in this paper, we introduce a bottom-up filtering approach exploiting the postfix commonality against the top-down approach of YFilter exploiting the prefix commonality. Some experimental results show that our method has better filtering performance when registered XPath queries mainly consist of the partial matching path queries with the postfix commonality.

For an uncertain discrete event system (DES) modeled as a set of some possible nondeterministic automata, we address robust supervisory control problems. Based on language models, this paper presents the existence conditions of a robust nonblocking (RN) supervisor that guarantees the absence of blocked states in a closed-loop system. We show that an RN supervisor achieves both a given language specification and the nonblocking characteristics of any nondeterministic automata of the set.

This paper presents a framework for the nonblocking supervisory control of nondeterministic discrete event systems (DESs) using multiple deterministic model. Necessary and sufficient conditions for the existence of a multiple model nonblocking supervisor are obtained for a multiple deterministic model. We show that a multiple model nonblocking supervisor guarantees the nonblockingness of an original nondeterministic system.

This paper introduces a probabilistic rebound automaton (pra), and investigates its accepting power and closure property. We show that (1) the class of languages recognized by pra's with error probability less than 1/2, PRA, is incomparable with the class of context-free languages, (2) there is a language accepted by a two-way nondeterministic one counter automaton, but not in PRA, and (3) there is a language accepted by a deterministic one-marker rebound automaton, but not in PRA. We also show that PRA is not closed under concatenation and Kleene + .

Over the last decade, research in the automatic synthesis and optimization of combinational logic has matured significantly; more recently, research has focused on sequential logic. Many of the paradigms for combinational logic have been extended and applied in the sequential domain. In addition, promising new directions for future research are being explored. In this paper, we survey some of the results of combinational synthesis and some recent results for sequential synthesis and then use these to view possible avenues for future sequential synthesis research. In particular we look at two related questions: deriving a set of permissible behaviors and using a minimizer to select the best behavior according to some optimization criteria. We examine these two issues in increasingly complex situations starting with a single-output function, and proceeding to a single multiple-output function, a network of single-output functions, a network of multiple-output functions, and then similar questions where function" is replaced by a finite state machine (FSM). We end with a discussion of a network of finite state machines and the problem of deriving the set of permissible FSM's and choosing a representative minimum one.

This paper reviews two topics of nonlinear system analysis done in Japan. The first half of this paper concerns with nonlinear system analysis through the nondeterministic operator theory. The nondeterministic operator is a set-valued or fuzzy set valued operator by K. Horiuchi. From 1975 Horiuchi has developed fixed point theorems for nondeterministic operators. Using such fixed point theorems, he developed a unique theory for nonlinear system analysis. Horiuchi's theory provides a fundamental view point for analysis of fluctuations in nonlinear systems. In this paper, it is pointed out that Horiuchi's theory can be viewed as an extension of the interval analysis. Next, Urabe's theory for nonlinear boundary value problems is discussed. From 1965 Urabe has developed a method of computer assisted existence proof for solutions of nonlinear boundary value problems. Urabe has presented a convergence theorem for a certain simplified Newton method. Urabe's theorem is essentially based on Banach's contraction mapping theorem. In this paper, reformulation of Urabe's theory using the interval analysis is presented. It is shown that sharp error estimation can be obtained by this reformulation. Both works discussed in this paper have been done independently with the interval analysis. This paper points out that they have deep relationship with the interval analysis. Moreover, it is also pointed out that these two works suggest future directions of the interval analysis.

The main result of this paper is an almost-everywhere hierarchy theorem for nondeterministic space that is as tight as the well-known infinitely-often hierarchy theorems for deterministic and nondeterministic space. In addition, we show that the complexity-theoretic notion of almost-everywhere complex functions is identical to the recursion-theoretic notion of bi-immune sets in the nondeterministic space domain. Finally, we investigate bi-immunity in nondeterministic and alternating time complexity classes and derive a similar hierarchy result for alternating time.

In the direct product space of a complete metric linear space X and its related space Y, a fuzzy mapping G is introduced as an operator by which we can define a projective fuzzy set G(x,y) for any xX and yY. An original system is represented by a completely continuous operator f(x)Y, e.g., in the form x=λ(f(x)), (λ is a linear operator), and a nondeterministic or fuzzy fluctuation induced into the original system is represented by a generalized form of system equation xβG(x,f(x)). By establishing a new fixed point theorem for the fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed here for the fluctuation problem goes beyond the scope of the perturbation theory.