Obradovic and Parberry showed that any n-input k-ary function can be computed by a depth 4 unit-weight k-ary threshold circuit of size O(nkn). They also showed that any n-input k-ary symmetric function can be computed by a depth 6 unit-weight k-ary threshold circuit of size O(nk+1). In this paper, we improve upon and expand their results. The k-ary threshold circuits of nonunit weight and unit weight are considered. We show that any n-input k-ary function can be computed by a depth 2 k-ary threshold circuit of size O(kn-1). This means that depth 2 is optimal for computing some k-ary functions (e.g., a PARITY function). We also show that any n-input k-ary function can be computed by a depth 3 unit-weight k-ary threshold circuit of size O(kn). Next, we show that any n-input k-ary symmetric function can be computed by a depth 3 k-ary threshold circuit of size O(nk-1), and can be computed by a depth 3 unit-weight k-ary threshold circuit of size O(knk-1). Finally, we show that if the weights of the circuit are polynomially bounded, some k-ary symmetric functions cannot be computed by any depth 2 k-ary threshold circuit of polynomial-size.

A Boolean network model is one of the models of gene regulatory networks, and is widely used in analysis and control. Although a Boolean network is a class of discrete-time nonlinear systems and expresses the synchronous behavior, it is important to consider the asynchronous behavior. In this paper, using a Petri net, a new modeling method of asynchronous Boolean networks with control inputs is proposed. Furthermore, the optimal control problem of Petri nets expressing asynchronous Boolean networks is formulated, and is reduced to an integer programming problem. The proposed approach will provide us one of the mathematical bases of control methods for gene regulatory networks.

Event-triggered and self-triggered control methods are an important control strategy in networked control systems. Event-triggered control is a method that the measured signal is sent to the controller (i.e., the control input is recomputed) only when a certain condition is satisfied. Self-triggered control is a method that the control input and the (non-uniform) sampling interval are computed simultaneously. In this paper, we propose new methods of event-triggered control and self-triggered control from the viewpoint of online optimization (i.e., model predictive control). In self-triggered control, the control input and the sampling interval are obtained by solving a pair of a quadratic programming (QP) problem and a mixed integer linear programming (MILP) problem. In event-triggered control, whether the control input is updated or not is determined by solving two QP problems. The effectiveness of the proposed methods is presented by numerical examples.

The symbolic model checking algorithm was proposed for the efficient verification of sequential circuits. In this paper, we show that this algorithm is applicable to the verification of concurrent systems described by finite capacity Petri nets. In this algorithm, specifications of the system are given in the form of temporal logic formulas, and the algorithm checks whether these formulas hold in the state space. All logical operations are performed on Binary Decision Diagrams. Since the algorithm does not enumerating each state, the problem of state space explosion can be avoided in many cases.

Just-in-time scheduling problem is the problem of finding an optimal schedule such that each job finishes exactly at its due date. We study the problem under a realistic assumption called periodic time slots. In this paper, we prove that this problem cannot be approximated, assuming P≠NP. Next, we present a heuristic algorithm, assuming that the number of machines is one. The key idea is a reduction of the problem to a network flow problem. The heuristic algorithm is fast because its main part consists of computation of the minimum cost flow that dominates the total time. Our algorithm is O(n3) in the worst case, where n is the number of jobs. Next, we show some simulation results. Finally, we show cases in which our algorithm returns an optimal schedule and is a factor 1.5 approximation algorithm, respectively, and also give an approximation ratio depending on the upper bound of set-up times.

Boolean networks (BNs) are considered as popular formal models for the dynamics of gene regulatory networks. There are many different types of BNs, depending on their updating scheme (synchronous, asynchronous, deterministic, or non-deterministic), such as Classical Random Boolean Networks (CRBNs), Asynchronous Random Boolean Networks (ARBNs), Generalized Asynchronous Random Boolean Networks (GARBNs), Deterministic Asynchronous Random Boolean Networks (DARBNs), and Deterministic Generalized Asynchronous Random Boolean Networks (DGARBNs). An important long-term behavior of BNs, so-called attractor, can provide valuable insights into systems biology (e.g., the origins of cancer). In the previous paper [1], we have studied properties of attractors of GARBNs, their relations with attractors of CRBNs, also proposed different algorithms for attractor detection. In this paper, we propose a new algorithm based on SAT-based bounded model checking to overcome inherent problems in these algorithms. Experimental results prove the effectiveness of the new algorithm. We also show that studying attractors of GARBNs can pave potential ways to study attractors of ARBNs.

Generating state spaces is one of important and general methods in the analysis of Petri nets. There are two reasons why state spaces of Petri nets become so large. One is concurrent occurring of transitions, and the other is periodic occurring of firing sequences. This paper focuses on the second problem, and proposes a new algorithm for exploring state spaces of finite capacity Petri nets with large capacities. In the proposed algorithm, the state space is represented in the form of a tree such that a set of markings generated by periodic occurrences of firing sequences is associated with each node, and it is much smaller than the reachability graph.

In this paper, we propose a new approximate algorithm for the model predictive control (MPC) problem with a time-varying reference of hybrid systems. The proposed algorithm consists of an offline computation and an online computation. In the offline computation, candidates of mode sequences are derived. In the online computation, after the mode sequence is uniquely decided among candidates, the finite-time optimal control problem, i.e., the quadratic programming problem, is solved. So by applying the proposed algorithm, the computational amount of the online computation is decreased. First, the MPC problem with a time-varying reference is formulated. Next, the proposed algorithm is explained, and the accuracy of the obtained approximate solution is discussed. Finally, the effectiveness of the proposed method is shown by a numerical example.

Software model checking is typically applied to components of large systems. The assumption generation is the problem of finding the least restrictive environment in which the components satisfy a given safety property. There is an algorithm to compute the environment for properties given as a regular language. In this paper, we propose a general scheme for computing the assumption even for non-regular properties, and show the uniqueness of the least restrictive assumption for any class of languages. In general, dealing with non-regular languages may fall into undecidability of problems. We also show a method to compute assumptions based on visibly pushdown automata and their finite-state abstractions.

Managing the configurations of complex systems consisting of various components requires the combined efforts by multiple domain experts. These experts have extensive knowledge about different components in the system they need to manage but little understanding of the issues outside their individual areas of expertise. As a result, the configuration constraints, changes, and procedures specified by those involved in the management of a complex system are often interrelated with one another without being noticed, and their integration into a coherent procedure for configuration represents a major challenge. The method of synthesizing the configuration procedure introduced in this paper addresses this challenge using a combination of formal specification and model finding techniques. We express the knowledge on system management with this method, which is provided by domain experts as first-order logic formulas in the Alloy specification language, and combine it with system-configuration information and the resulting specification. We then employ the Alloy Analyzer to find a system model that satisfies all the formulas in this specification. The model obtained corresponds to a procedure for system configurations that satisfies all expert-specified constraints. In order to reduce the resources needed in the procedure synthesis, we reduce the length of procedures to be synthesized by defining and using intermediate goal states to divide operation procedures into shorter steps. Finally, we evaluate our method through a case study on a procedure to consolidate virtual machines.

In this paper, we present a new method for diagnosis of stochastic discrete event system. The method is based on anomaly detection for sequences. We call the method sequence profiling (SP). SP does not require any system models and any system-specific knowledge. The only information necessary for SP is event logs from the target system. Using event logs from the system in the normal situation, N-gram models are learned, where the N-gram model is used as approximation of the system behavior. Based on the N-gram model, the diagnoser estimates what kind of faults has occurred in the system, or may conclude that no faults occurs. Effectiveness of the proposed method is demonstrated by application to diagnosis of a multi-processor system.

Boarding is the last step of aircraft turnaround and its completion in the shortest possible time is desired. In this paper, we propose a new boarding strategy that outperforms conventional strategies such as the back-to-front strategy and the outside-in strategy. The Steffen method is known as one of the most efficient boarding strategies in literature, but it is hard to be realized in the real situation because the complete sorting of passengers in a prescribed order is required. The proposed strategy shows a performance close to that of the Steffen method and can be easily implemented by using a special gate system.

In previous papers by the authors, a new scheme for diagnosis of stochastic discrete event systems, called sequence profiling (SP), is proposed. From given event logs, N-gram models that approximate the behavior of the target system are extracted. N-gram models are used for discovering discrepancy between observed event logs and the behavior of the system in the normal situation. However, when the target system is a distributed system consisting of several subsystems, event sequences from subsystems may be interleaved, and SP cannot separate the faulty event sequence from the interleaved sequence. In this paper, we introduce wildcard characters into event patterns. This contributes to removing the effect by subsystems which may not be related to faults.

This paper investigates a relationship between inkdot and one-pebble for two-dimensional finite automata (2-fa's). Especially we show that (1) alternating inkdot 2-fa's are more powerful than nondeterministic one-pebble 2-fa's, and (2) there is a set accepted by an alternating inkdot 2-fa, but not accepted by any alternating one-pebble 2-fa with only universal states.

In this paper, we study performance evaluation of workflow-based information systems. Because of state space explosion, analysis by stochastic models, such as stochastic Petri nets and queuing models, is not suitable for workflow systems in which a large number of flow instances run concurrently. We use fluid-flow approximation technique to overcome this difficulty. In the proposed method, GSPN (Generalized Stochastic Petri Nets) models representing workflows are approximated by a class of timed continuous Petri nets, called routing timed continuous Petri nets (RTCPN). In RTCPN models, each discrete set is approximated by a continuous region on a real-valued vector space, and variance in probability distribution is replaced with a real-valued interval. Next we derive piecewise linear systems from RTCPN models, and use interval methods to compute guaranteed enclosures for state variables. As a case study, we solve an optimal resource assignment problem for a paper review process.

We study analysis of hybrid systems under incomplete knowledge. The class of hybrid systems to be considered is assumed to have the form of a rectangular hybrid automaton such that each constant in invariants and guards is given as a parameter. We develop a method based on symbolic computation that computes an approximation of the discrete behavior of the automaton. We also show an implementation on a constraint logic programming language.

State space explosion is a serious problem in analyzing discrete event systems that allow concurrent occurring of events. A new method is proposed for generating reduced state spaces of systems. This method is an improvement of Valmari's stubborn set method. The generated state space preserves liveness, livelocks, and terminal states of the ordinary state space. Petri nets are used as a model of systems, and a method is shown for generating a reduced state space from a given Petri net.

Agent technology is widely recognized as a new paradigm for the design of concurrent software and systems. The aim of this paper is to give a mathematical foundation for the design and the analysis of multi-agent systems by means of a Petri-net-based model. The proposed model, called PN2, is based on place/transition nets (P/T nets), which is one of the simplest classes of Petri nets. The main difference of PN2's from P/T nets is that each token, representing an agent, is also a P/T net. PN2's are sufficiently simple for the mathematical analysis, such as invariant analysis, but have enough modeling power.

The legal firing sequence problem of Petri nets (LFS) is one of fundamental problems in the analysis of Petri nets, because it appears as a subproblem of various basic problems. Since LFS is shown to be NP-hard, various heuristics has been proposed to solve the problem of practical size in a reasonable time. In this paper, we propose a new algorithm for this problem. It is based on the partial order verification technique, and reduces redundant branches in the search tree. Moreover, the proposed algorithm can be combined with various types of heuristics.

In this paper, we propose a new modeling method to express discrete-time hybrid systems with parameter uncertainty as a mixed logical dynamical (MLD) model. In analysis and control of hybrid systems, there are problem formulations in which convex polyhedra are computed, but for high-dimensional systems, it is difficult to solve these problems within a practical computation time. The key idea of this paper is to use an interval method, which is one of the classical methods in verified numerical computation, and to regard an interval as an over-approximation of a convex polyhedron. By using the obtained MLD model, analysis and synthesis of robust control systems are formulated.