Infinite Time Turing Machines

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.     

Structured Turing Machines

The concept of a structured Turing machine is introduced. Every Turing machine is demonstrated to be equivalent to some structured Turing machine. Various refinements of the problem of structurization are considered and, in particular, refinements in which any extension of the working alphabet being used is prohibited.     

Accelerating Turing Machines

Minds and Machines - Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine...     

Transcending Turing Computability

It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing-machine computation; proofs have been offered on both sides, subject to differing assumptions. In this article I argue that the important comparisons between the two models of computation are not so much mathematical as epistemological. The Turing-machine model makes assumptions about information representation and processing that are badly matched to the realities of natural computation (information representation and processing in or inspired by natural systems). This points to the need for new models of computation addressing issues orthogonal to those that have occupied the traditional theory of computation.     

Three-dimensional parallel Turing machines

Informally, the parallel Turing machine (PTM) proposed by Wiedermann is a set of identical usual sequential Turing machines (STMs) cooperating on two common tapes: storage tape and input tape. Moreover, STMs which represent the individual processors of a parallel computer can multiply themselves in the course of computation. On the other hand, during the past 25 years or so, automata on a three-dimensional tape have been proposed as computational models of three-dimensional pattern processing, and several properties of such automata have been obtained. We proposed a three-dimensional parallel Turing machine (3-PTM), and dealt with a hardware-bounded 3-PTM whose inputs are restricted to cubic ones. We believe that this machine is useful in measuring the parallel computational complexity of three-dimensional images. In this article, we continue the study of 3-PTM, whose inputs are restricted to cubic ones, and investigate some of its accepting powers. This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007     

Some accepting powers of three-dimensional parallel Turing machines

Informally, the parallel Turing machine (PTM) proposed by Wiedermann is a set of identical usual sequential Turing machines (STMs) cooperating on two common tapes: storage tape and input tape. Moreover, STMs which represent the individual processors of a parallel computer can multiply themselves in the course of computation. On the other hand, during the past 25 years or so, automata on a three-dimensional tape have been proposed as computational models of three-dimensional pattern processing, and several properties of such automata have been obtained. We proposed a three-dimensional parallel Turing machine (3-PTM),¹ and dealt with a hardware-bounded 3-PTM whose inputs are restricted to cubic ones. We believe that this machine is useful in measuring the parallel computational complexity of three-dimensional images. Here, we continue the study of 3-PTM, whose inputs are restricted to cubic ones, and investigate some of its accepting powers. This work was presented in part at the First European Workshop on Artificial Life and Robotics, Vienna, Austria, July 12–13, 2007     

Turing machines, transition systems, and interaction

This paper presents persistent Turing machines (PTMs), a new way of interpreting Turing-machine computation, based on dynamic stream semantics. A PTM is a Turing machine that performs an infinite sequence of “normal” Turing machine computations, where each such computation starts when the PTM reads an input from its input tape and ends when the PTM produces an output on its output tape. The PTM has an additional worktape, which retains its content from one computation to the next; this is what we mean by persistence.A number of results are presented for this model, including a proof that the class of PTMs is isomorphic to a general class of effective transition systems called interactive transition systems; and a proof that PTMs without persistence (amnesic PTMs) are less expressive than PTMs. As an analogue of the Church-Turing hypothesis which relates Turing machines to algorithmic computation, it is hypothesized that PTMs capture the intuitive notion of sequential interactive computation.     

离散II-型模糊集的不确定性度量

随着II-型模糊集理论的不断发展和应用领域的扩大,需要探讨II-型模糊集不确定性的性质与度量方法,在研究II-型模糊集不确定性特征及模糊熵的基础上,通过扩展模糊熵的定义,给出了离散II-型模糊集熵的定义,证明其满足模糊熵的4条公理性条件,该定义将对II-型模糊集在不确定环境中的应用提供新的思路和方法。     

Minds, Machines and Turing

Turing's celebrated 1950 paper proposes a very generalmethodological criterion for modelling mental function: total functionalequivalence and indistinguishability. His criterion gives rise to ahierarchy of Turing Tests, from subtotal (toy) fragments of ourfunctions (t1), to total symbolic (pen-pal) function (T2 – the standardTuring Test), to total external sensorimotor (robotic) function (T3), tototal internal microfunction (T4), to total indistinguishability inevery empirically discernible respect (T5). This is areverse-engineering hierarchy of (decreasing) empiricalunderdetermination of the theory by the data. Level t1 is clearly toounderdetermined, T2 is vulnerable to a counterexample (Searle's ChineseRoom Argument), and T4 and T5 are arbitrarily overdetermined. Hence T3is the appropriate target level for cognitive science. When it isreached, however, there will still remain more unanswerable questionsthan when Physics reaches its Grand Unified Theory of Everything (GUTE),because of the mind/body problem and the other-minds problem, both ofwhich are inherent in this empirical domain, even though Turing hardlymentions them.     

Effective Computation by Humans and Machines

There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing argument for CTT by analyzing the processes carried out by a human computer. I then contend that if the Gandy–Sieg account is correct, then the notion of effective computability has changed after 1936. Today computer scientists view effective computability in terms of finite machine computation. My contention is supported by the current formulations of CTT, which always refer to machine computation, and by the current argumentation for CTT, which is different from the main arguments advanced by Turing and Church. I finally turn to discuss Robin Gandy's characterization of machine computation. I suggest that there is an ambiguity regarding the types of machines Gandy was postulating. I offer three interpretations, which differ in their scope and limitations, and conclude that none provides the basis for claiming that Gandy characterized finite machine computation.     

Type-2 fuzzy Gaussian mixture models

This paper presents a new extension of Gaussian mixture models (GMMs) based on type-2 fuzzy sets (T2 FSs) referred to as T2 FGMMs. The estimated parameters of the GMM may not accurately reflect the underlying distributions of the observations because of insufficient and noisy data in real-world problems. By three-dimensional membership functions of T2 FSs, T2 FGMMs use footprint of uncertainty (FOU) as well as interval secondary membership functions to handle GMMs uncertain mean vector or uncertain covariance matrix, and thus GMMs parameters vary anywhere in an interval with uniform possibilities. As a result, the likelihood of the T2 FGMM becomes an interval rather than a precise real number to account for GMMs uncertainty. These interval likelihoods are then processed by the generalized linear model (GLM) for classification decision-making. In this paper we focus on the role of the FOU in pattern classification. Multi-category classification on different data sets from UCI repository shows that T2 FGMMs are consistently as good as or better than GMMs in case of insufficient training data, and are also insensitive to different areas of the FOU. Based on T2 FGMMs, we extend hidden Markov models (HMMs) to type-2 fuzzy HMMs (T2 FHMMs). Phoneme classification in the babble noise shows that T2 FHMMs outperform classical HMMs in terms of the robustness and classification rate. We also find that the larger area of the FOU in T2 FHMMs with uncertain mean vectors performs better in classification when the signal-to-noise ratio is lower.     

Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization

In many real-world problems involving pattern recognition, system identification and modeling, control, decision making, and forecasting of time-series, available data are quite often of uncertain nature. An interesting alternative is to employ type-2 fuzzy sets, which augment fuzzy models with expressive power to develop models, which efficiently capture the factor of uncertainty. The three-dimensional membership functions of type-2 fuzzy sets offer additional degrees of freedom that make it possible to directly and more effectively account for model’s uncertainties. Type-2 fuzzy logic systems developed with the aid of evolutionary optimization forms a useful modeling tool subsequently resulting in a collection of efficient “If-Then” rules.The type-2 fuzzy neural networks take advantage of capabilities of fuzzy clustering by generating type-2 fuzzy rule base, resulting in a small number of rules and then optimizing membership functions of type-2 fuzzy sets present in the antecedent and consequent parts of the rules. The clustering itself is realized with the aid of differential evolution.Several examples, including a benchmark problem of identification of nonlinear system, are considered. The reported comparative analysis of experimental results is used to quantify the performance of the developed networks.     

用MapX访问Oracle中的空间数据

采用数据库管理空间数据是当前的发展趋势,文中总结了Oracle数据库中空间数据的上载和存储机制,探讨了应用程序对Oracle数据库中空间数据的访问,并给出应用实例。     

Interval Type-2 fuzzy voter design for fault tolerant systems

A voting scheme constitutes an essential component of many fault tolerant systems. Two types of voters are commonly used in applications of real-valued systems: the inexact majority and the amalgamating voters. The inexact majority voter effectively isolates erroneous modules and is capable of reporting benign outputs when a significant disagreement is detected. However, an application specific voter threshold must be provided. On the other hand, amalgamating voter, such as the weighted average voter, reduces the influence of faulty modules by averaging the input values together. Unlike the majority voters, amalgamating voters are not capable of producing benign outputs. In the past, a Type-1 (T1) fuzzy voting scheme was introduced, allowing for both smooth amalgamation of voter inputs and effective signalization of benign outputs. The presented paper proposes an extension to the fuzzy voting scheme via incorporating Interval Type-2 (IT2) fuzzy logic. The IT2 fuzzy logic allows for an improved handling of uncertain assumptions about the distributions of noisy and erroneous inputs which are essential for correct design of the fuzzy voting scheme. The proposed voter design features robust performance when the uncertainty assumptions dynamically change over time. The IT2 fuzzy voter architecture was compared against the average voter, inexact majority voter, and the T1 fuzzy voter using a refined experimental harness. The reported results demonstrate improved availability, safety and reliability of the presented IT2 fuzzy voting scheme.     

Type-2 fuzzy logic based urban traffic management

This paper presents a multi-agent system based on type-2 fuzzy decision module for traffic signal control in a complex urban road network. The distributed agent architecture using type-2 fuzzy set based controller was designed for optimizing green time in a traffic signal to reduce the total delay experienced by vehicles. A section of the Central Business District of Singapore simulated using PARAMICS software was used as a test bed for validating the proposed agent architecture for the signal control. The performance of the proposed multi-agent controller was compared with a hybrid neural network based hierarchical multi-agent system (HMS) controller and real-time adaptive traffic controller (GLIDE) currently used in Singapore. The performance metrics used for evaluation were total mean delay experienced by the vehicles to travel from source to destination and the current mean speed of vehicles inside the road network. The proposed multi-agent signal control was found to produce a significant improvement in the traffic conditions of the road network reducing the total travel time experienced by vehicles simulated under dual and multiple peak traffic scenarios.     

Type-2 Fuzzy Logic Control of a Flexible-Joint Manipulator

A type-2 fuzzy logic controller (FLC) is proposed in this article for robot manipulators with joint elasticity and structured and unstructured dynamical uncertainties. The proposed controller is based on a sliding mode control strategy. To enhance its real-time performance, simplified interval fuzzy sets are used. The efficiency of the control scheme is further enhanced by using computationally inexpensive input signals independently of the noisy torque and acceleration signals, and by adopting a trade off strategy between the manipulator’s position and the actuators’ internal stability. The controller is validated through a set of numerical experiments and by comparing it against its type-1 counterpart. It is shown through these experiments the higher performance of the type-2 FLC in compensating for larger magnitudes of uncertainties with severe nonlinearities. This work was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Microelectronics Corporation (CMC).     

区间数的区间Ⅱ型模糊c均值聚类算法

针对区间数模糊c均值聚类算法存在模糊度指数m无法准确描述数据簇划分情况的问题,对点数据集合的区间Ⅱ型模糊c均值聚类算法进行拓展,将其扩展到区间型不确定数据的聚类中。同时,分析了区间数的区间Ⅱ型模糊c均值聚类算法的收敛性,以确定模糊度指数m1和m2的取值原则。基于合成数据和实测数据的仿真实验结果表明：区间数的区间Ⅱ型模糊c均值聚类算法比区间数的模糊c均值聚类算法的聚类效果好。     

DB2与Oracle数据库技术的对比研究

本文根据数据仓库的任务、特点和应该具备的关键能力，对DB2和Oracle两大数据库的数据仓库技术在索引能力、数据分区、仓库管理器等方面进行了对比研究。