模糊自动机的强连通性及群自动机

为了更好地研究模糊自动机的结构和性质,采用代数的方法,在传统的模糊有限状态自动机的基础上,通过定义状态集合为代数群的自动机,讨论了这一类自动机的连通性和正则性,这丰富了模糊自动机理论．     

Edge-minimization of non-deterministic finite automata

In this paper we consider non-deterministic finite Rabin-Scott’s automata. We use a special structure to describe all the possible edges of non-deterministic finite automaton defining the given regular language. Such structure can be used for solving various problems of finite automata theory. One of these problems is edge-minimization of non-deterministic automata. As we have not touched this problem before, we obtain here two versions of the algorithm for solving this problem to continue previous series of articles.     

Some properties of the basis finite automaton

The present paper discusses non-deterministic finite Rabin-Scott’s automata. The majority of works recently dealing with this subject were, in fact, concerned only with properties of a canonical form automata or of some objects equivalent to it. This article continues the series of works in which the authors state a different point of view, describing the finite automata as just another invariant of the given regular language called basis finite automaton. In this article the authors argue on some new properties for the basis finite automaton. One of them is included into basis automaton’s table of binary relations. It is stated that this table can not contain either identical strings or identical columns. Another property depicts a possibility to obtain any finite automaton for a given regular language by the process of duplicating or combining some of its states.     

基于模糊字符串的Mealy格值有限自动机及其最小化

提出取值为格半群的Mealy格值有限自动机的概念,进而得到基于模糊字符串的Mealy格值有限自动机的扩张模型,并较详细讨论了其性质. 同时定义了扩张的完备Mealy格值有限自动机的行为矩阵, 在此基础上给出了其最小化算法.     

具有输出字符功能的模糊自动机的最小化问题

通过文献[8]中两类具有输出字符功能的Fuzzy自动机和Fuzzy有限状态自动机的强等价性,等价性和弱等价性的条件,在以往仅仅给出的Fuzzy有限状态自动机的最小化问题基础上,讨论了具有更广泛意义的具有输出字符功能的Fuzzy自动机的最小化问题,以及其最小化自动机与Fuzzy有限状态自动机的最小化自动机在不同条件下的关系。     

Bottom-up design of strategic options as finite automata

In this paper we look at the problem of strategic decision making. We start by presenting a new formalisation of strategic options as finite automata. Then, we show that these finite automata can be used to develop complex models of interacting options, such as option combinations and product options. Finally, we analyse real option games, presenting an algorithm to generate option games (based on automata).     

A fast algorithm for robust regression with penalised trimmed squares

The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked high leverage outliers in finite samples. An alternative to the LTS estimator, called Penalised Trimmed Squares (PTS) estimator, was introduced by the authors in Zioutas and Avramidis (2005) Acta Math Appl Sin 21:323–334, Zioutas et al. (2007) REVSTAT 5:115–136 and it appears to be less sensitive to the masking problem. This estimator is defined by a Quadratic Mixed Integer Programming (QMIP) problem, where in the objective function a penalty cost for each observation is included which serves as an upper bound on the residual error for any feasible regression line. Since the PTS does not require presetting the number of outliers to delete from the data set, it has better efficiency with respect to other estimators. However, due to the high computational complexity of the resulting QMIP problem, exact solutions for moderately large regression problems is infeasible. In this paper we further establish the theoretical properties of the PTS estimator, such as high breakdown and efficiency, and propose an approximate algorithm called Fast-PTS to compute the PTS estimator for large data sets efficiently. Extensive computational experiments on sets of benchmark instances with varying degrees of outlier contamination, indicate that the proposed algorithm performs well in identifying groups of high leverage outliers in reasonable computational time.     

Computing Approximating Automata for a Class of Hybrid Systems

This paper presents a new algorithm for generating finite-state automata models of hybrid systems in which the continuous-state dynamics can be switched when the continuous-state trajectory generates threshold events. The automata state transitions correspond to threshold events and the automata states correspond to portions of the threshold surfaces in the continuous state space. The hybrid system dynamics are approximated by the automata models in the sense that the languages of threshold event sequences generated by the automata contain the threshold event language for the hybrid system. Properties of the algorithm for constructing and refining the approximating automata are demonstrated and the application of approximating automata for system verification is illustrated for a switching controller for an inverted pendulum. Relationships to other approaches to hybrid system synthesis and verification are also discussed.     

On-line identification of language measure parameters for discrete-event supervisory control

The discrete-event dynamic behavior of physical plants is often represented by regular languages that can be realized as deterministic finite state automata (DFSA). The concept and construction of signed real measures of regular languages have been recently reported in literature. Major applications of the language measure are: quantitative evaluation of the discrete-event dynamic behavior of unsupervised and supervised plants; and analysis and synthesis of optimal supervisory control algorithms in the discrete-event setting. This paper formulates and experimentally validates an on-line procedure for identification of the language measure parameters based on a DFSA model of the physical plant. The recursive algorithm of this identification procedure relies on observed simulation and/or experimental data. Efficacy of the parameter identification procedure is demonstrated on the test bed of a mobile robotic system, whose dynamic behavior is modelled as a DFSA for discrete-event supervisory control.     

基于矩阵模型表示的(线性)有限自动机的同步序列判定

在有限自动机矩阵模型表示方法的基础上,采用矩阵理论和布尔代数为工具,分别给出了判定输入序列是否是(线性)有限自动机的同步序列的新充要条件和求解线性有限自动机的最短同步序列的新算法.     

非参数回归函数的稳健Bootstrap

在有异常值的数据中,Bootstrap样本可能比原有样本含有更高的“污染”,这会降低所要做的统计推断的有效性.本文讨论在非参数回归N-W估计中,如何利用影响函数得到重新抽样的概率,使用倾斜的Bootstrap方法得到曲线的拟合,从而达到有效地抵制异常值对回归函数影响的目的,数值模拟的结果表明这种处理方式的有效性.     

The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother

A Gaussian-sum smoother is developed based on the two filter formula for smoothing. This facilitates the application of non-Gaussian state space modeling to diverse problems in time series analysis. It is especially useful when a higher order state vector is required and the application of the non-Gaussian smoother based on direct numerical computation is impractical. In particular, applications to the non-Gaussian seasonal adjustment of economic time series and to the modeling of seasonal time series with several outliers are shown.     

Minimization algorithm of fuzzy finite automata

In this paper, a class of fuzzy finite automata corresponding to the Mealy type of ordinary automata is formulated, and also two types of statewise equivalence relations are introduced. From the equivalence relations, a minimal form is defined and a minimization algorithm of the Mealy type of fuzzy finite automata is obtained.     

Baxter-Guttmann-Jensen conjecture for power series in directed percolation problem

A probabilistic model of a flow of fluid through a random medium,percolation model, provides a typical example of statistical mechanical problems which are easy to describe but difficult to solve. While the percolation problem on undirected planar lattices is exactly solved as a limit of the Potts models, there still has been no exact solution for the directed lattices. The most reliable method to provide good approximations is a numerical estimation using finite power-series expansion data of the infinite formal power series for percolation probability. In order to calculate higher-order terms in power series, Baxter and Guttmann [6] and Jensen and Guttmann [33] proposed an extrapolation procedure based on an assumption that thecorrection terms, which show the difference between the exact infinite power series and approximate finite series, are expressed as linear combinations of the Catalan numbers.In this paper, starting from a brief review on the directed percolation problem and the observation by Baxter, Guttmann, and Jensen, we state some theorems in which we explain the reason why the combinatorial numbers appear in the correction terms of power series. In the proof of our theorems, we show several useful combinatorial identities for the ballot numbers, which become the Catalan numbers in a special case. These identities ensure that a summation of products of the ballot numbers with polynomial coefficients can be expanded using the ballot numbers. There is still a gap between our theorems and the Baxter-Guttmann-Jensen observation, and we also give some conjectures.As a generalization of the percolation problem on a directed planar lattice, we present two topics at the end of this paper: The friendly walker problem and the stochastic cellular automata in higher dimensions. We hope that these two topics as well as the directed percolation problem will be of much interest to researchers of combinatorics.     

Spectral density estimation with amplitude modulation and outlier detection

This paper studies spectral density estimation based on amplitude modulation including missing data as a specific case. A generalized periodogram is introduced and smoothed to give a consistent estimator of the spectral density by running local linear regression smoother. We explore the asymptotic properties of the proposed estimator and its application to time series data with periodic missing. A simple data-driven local bandwidth selection rule is proposed and an algorithm for computing the spectral density estimate is presented. The effectiveness of the proposed method is demonstrated using simulations. The application to outlier detection based on leave-one-out diagnostic is also considered. An illustrative example shows that the proposed diagnostic procedure succeeds in revealing outliers in time series without masking and smearing effects. Supported by Chinese NSF Grants 10001004 and 39930160, and Fellowship of City University of Hong Kong.     

Automata on ordinals and automaticity of linear orders

We investigate structures recognizable by finite state automata with an input tape of length a limit ordinal. At limits, the set of states which appear unboundedly often before the limit are mapped to a limit state. We describe a method for proving non-automaticity and apply this to determine the optimal bounds for the ranks of linear orders recognized by such automata.     

A Finite Field Framework for Modeling,Analysis and Control of Finite State Automata

In this paper, we address the modeling, analysis and control of finite state automata, which represent a standard class of discrete event systems. As opposed to graph theoretical methods, we consider an algebraic framework that resides on the finite field <formula form="inline">${\Op F}_2$</formula> which is defined on a set of two elements with the operations addition and multiplication, both carried out modulo 2. The key characteristic of the model is its functional completeness in the sense that it is capable of describing most of the finite state automata in use, including non-deterministic and partially defined automata. Starting from a graphical representation of an automaton and applying techniques from Boolean algebra, we derive the transition relation of our finite field model. For cases in which the transition relation is linear, we develop means for treating the main issues in the analysis of the cyclic behavior of automata. This involves the computation of the elementary divisor polynomials of the system dynamics, and the periods of these polynomials, which are shown to completely determine the cyclic structure of the state space of the underlying linear system. Dealing with non-autonomous linear systems with inputs, we use the notion of feedback in order to specify a desired cyclic behavior of the automaton in the closed loop. The computation of an appropriate state feedback is achieved by introducing an image domain and adopting the well-established polynomial matrix method to linear discrete systems over the finite field <formula form="inline">${\Op F}_2$</formula>. Examples illustrate the main steps of our method.     

The Automata that Define Representations of Monomial Algebras

It is well known that the sets of strings that define all representations of string algebras and many representations of other quotients of path algebras form a regular set, and hence are defined by finite state automata. This short article aims to explain this connection between representation theory and automata theory in elementary terms; no technical background in either representation theory or automata theory is assumed. The article describes the structure of the set of strings of a monomial algebra as a locally testable and hence regular set, and describes explicitly the construction of the automaton, illustrating the construction with an elementary example. Hence it explains how the sets of strings and bands of a monomial algebra correspond to the sets of paths and closed (non-powered) circuits in a finite graph, and how the growth rate of the set of bands is immediately visible from that graph. Presented by C. Ringel.     

增量式Huber-支持向量回归机算法研究

传统的面向支持向量回归的一次性建模算法中样本增加时,均需从头开始学习,而增量式算法可以充分利用上一阶段的学习成果。SVR的增量算法通常基于ε-不敏感损失函数,该损失函数对大的异常值比较敏感,而Huber损失函数对异常值敏感度低。所以在有噪声的情况下,Huber损失函数是比ε-不敏感损失函数更好的选择,在现实情况当中。基于此,本文提出了一种基于Huber损失函数的增量式Huber-SVR算法,该算法能够持续地将新样本信息集成到已经构建好的模型中,而不是重新建模。与增量式ε-SVR算法和增量式RBF算法相比,在对真实数据进行预测建模时,增量式Huber-SVR算法具有更高的预测精度。     

Detecting multiple outliers in linear regression using a cluster method combined with graphical visualization

This paper provides a graphical visualization of multiple outliers based on a clustering algorithm using the minimal spanning tree, and proposes a modified version of this clustering algorithm for identifying multiple outliers. Graphical visualization is helpful for the classification of multiple outliers. It is shown that the proposed modified procedure preserves the performance of the clustering algorithm in identifying multiple outliers, but also reduces the problem of swamping of observations.