Computing presentations for subgroups of polycyclic groups and of context-free groups

Algorithms for solving uniform decision problems for algebraic structures crucially depend on the chosen finite presentations for the structures under consideration. Rewriting techniques have been used very successfully to solve uniform decision problems, when the presentations considered involve finite, noetherian, and ()-confluent rewriting systems. Whenever the class of algebraic structures considered is closed under the operation of taking finitely generated substructures, then the algorithms for solving the uniform decision problems can be applied to the substructures as well. However, since these algorithms depend on the form of the presentations, this involves the task of constructing a presentation of a certain form for a substructure given a presentation of this form for the structure itself and a finite set of generating elements for the substructure.This problem, which has received a lot of attention in algebra, is here investigated from an algorithmic point of view. The structures considered are the following two classes of groups, which have been studied extensively before: the polycyclic groups and the context-free groups.Finitely generated context-free groups can be presented by finite, monadic, and -confluent string-rewriting systems. Due to their nice algorithmic properties these systems provide a way to effectively solve many decision problems for context-free groups. Since finitely generated subgroups of context-free groups are again contextfree, they can be presented in the same way. Here we describe a process that, from a finite, monadic, and -confluent string-rewriting system presenting a context-free groupG and a finite subsetU ofG, determines a presentation of this form for the subgroup U ofG that is generated byU. For finitely presented polycyclic groups we obtain an analogous result, when we use finite confluent PCP2-presentations to describe these groups.This work was performed while this author was visiting at the Fachbereich Informatik, Universität Kaiserslautern, during his sabbatical 1991/92     

Japanese educational and learning systems in the post-industrial society: A value chain of educational and learning systems

Japan's educational system has some major problems. The most important among these concerns is the basic concept of the educational process and the goal of education. The old concept of public educational systems has become outdated in today's Japanese society, although this concept had supported social and spiritual faith, economic success and selfless devotion to one's country for more than 100 years. Now, Japanese people need a new concept of the educational process and the goal of education for the twenty-first century. The paper proposes a value chain of educational and learning systems aimed at building a network consisting of multiple fields for fostering future human resources.     

ARPO-2: An expert system for legal advice on the breach of building contracts

Although Berman and Hafner [Berman 1989, pp. 928–938] presented the possibility to adapt the model of reasoning of development of an expert system for medical diagnosis to the reasoning of a judge when he/she sentences criminals does not resemble the reasoning found in the decisions of physicians, mathematicians or statisticians.When a lawyer reasons, he/she not only looks for the solution of a case; he/she simultaneously looks for the bases on which his/her reasoning can rest [Galindo 1992, pp. 363–367]. That is to say, he/she not only needs to find the solution but moreover he/she has to find the references (laws, jurisprudence and bibliography) that allow him/her to argue the solution.In many cases, computer solutions to these reasoning processes have been made in a separated way: the solution to the cases using expert systems, and the search of documentation using information retrieval systems.This paper presents the ARPO-2 prototype, a solution integrating the two aspects of legal reasoning: an expert system which is able to simultaneously find the solution to a problem and to give the necessary references so that the lawyer argues the solution. The subject on which the prototype solves problems is the breach of building contracts.In this paper, we describe the process of development of an expert system for solving, justification and documentation of breach of contracts, giving details on the way how the objects that intervene in the case were defined as well as on the reasoning followed.This paper was funded in part by DGICYT, Spanish Civil Law Computerization Project: PB870-632.     

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems.A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input.An adaptive asymptotically stabilizing controller,which can guarantee the stability of the closed-loop system and the convergence of the original system state,is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) an...     

Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control

The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.     

Multi-level hierarchical interface-based supervisory control

Hierarchical Interface-Based Supervisory Control employs interfaces that allow properties of a monolithic system to be verified through local analysis. By avoiding the need to verify properties globally, significant computational savings can be achieved. In this paper we provide local requirements for a multi-level architecture employing command-pair type interfaces. This multi-level architecture allows for a greater reduction in complexity and improved reconfigurability over the two-level case that has been previously studied since it allows the global system to be partitioned into smaller modules. This paper also provides results for synthesizing supervisors in the multi-level architecture that are locally maximally permissive with respect to a given specification and set of interfaces.     

Semi‐global output feedback tracking control for fully actuated ships

An output feedback trajectory tracking controller for a kind of 3 degrees of freedom (DOF) ship motion nonlinear model is designed. The closed‐loop control system is proven to be uniformly semi‐globally exponential stable with a separate stability result for the observer by applying nonlinear cascaded system theory. Simulation results on a model ship, Cybership II, are presented to validate the proposed control scheme. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A characterization of (regular) circular languages generated by monotone complete splicing systems

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for monotone complete systems, which are finite circular splicing systems with rules of a simpler form. We show that a circular language L is generated by a monotone complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by monotone complete systems. We can also decide whether the language generated by a monotone complete system is regular. Finally, we point out that monotone complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule of a specific type is allowed. From our results on monotone complete systems, it follows that finite simple systems generate a class of languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems.     

A quantitative multimodal discourse analysis of teaching and learning in a web-conferencing environment – The efficacy of student-centred learning designs

This paper presents a quantitative approach to multimodal discourse analysis for analyzing online collaborative learning. The coding framework draws together the fields of systemic functional linguistics and Activity Theory to analyze interactions between collaborative-, content- and technology-related discourse. The approach is used to examine how the task subject matter, the activity design, and the choice of interface affected interaction and collaboration for a computing course conducted in a web-conferencing environment. The analysis revealed the critical impact of activity design on the amount and type of discourse that transpired. Student-centred designs resulted in over six times more student discourse as compared to teacher-centred designs and created a learning environment where students took greater ownership over the tasks and contributed more to the content-based discussion. The paper also incorporates a rationale for the approach to coding and a reflection on its efficacy for discourse analysis in technology-based learning environments.