A Characterization of ET0L and EDT0L Languages

There exists a PT0L language $L_0$ such that the following holds. A language $L$ is an ET0L language if and only if there exists a mapping $T$ induced by an a-NGSM (nondeterministic generalized sequential machine with accepting states) such that $L = T(L_0)$. There exists an infinite collection of EPDT0L languages $D_{mn}\subseteq\Sigma_{mn}^\star$ ($n\geq m\geq 1$) such that the family EDT0L is characterized in the following way. A language $L$ is an EDT0L language if and only if there exists $n\geq m\geq 1$, a homomorphism $h$ and a regular language $R \subseteq \Sigma_{mn}^\star$ such that $L = h(D_{mn} \cap R)$.\u

L-systems in Geometric Modeling

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Contributions of formal language theory to the study of dialogues

For more than 30 years, the problem of providing a formal framework for modeling dialogues has been a topic of great interest for the scientific areas of Linguistics, Philosophy, Cognitive Science, Formal Languages, Software Engineering and Artificial Intelligence. In the beginning the goal was to develop a "conversational computer", an automated system that could engage in a conversation in the same way as humans do. After studies showed the difficulties of achieving this goal Formal Language Theory and Artificial Intelligence have contributed to Dialogue Theory with the study and simulation of machine to machine and human to machine dialogues inspired by Linguistic studies of human interactions. The aim of our thesis is to propose a formal approach for the study of dialogues. Our work is an interdisciplinary one that connects theories and results in Dialogue Theory mainly from Formal Language Theory, but also from another areas like Artificial Intelligence, Linguistics and Multiprogramming. We contribute to Dialogue Theory by introducing a hierarchy of formal frameworks for the definition of protocols for dialogue interaction. Each framework defines a transition system in which dialogue protocols might be uniformly expressed and compared. The frameworks we propose are based on finite state transition systems and Grammar systems from Formal Language Theory and a multi-agent language for the specification of dialogue protocols from Artificial Intelligence. Grammar System Theory is a subfield of Formal Language Theory that studies how several (a finite number) of language defining devices (language processors or grammars) jointly develop a common symbolic environment (a string or a finite set of strings) by the application of language operations (for instance rewriting rules). For the frameworks we propose we study some of their formal properties, we compare their expressiveness, we investigate their practical application in Dialogue Theory and we analyze their connection with theories of human-like conversation from Linguistics. In addition we contribute to Grammar System Theory by proposing a new approach for the verification and derivation of Grammar systems. We analyze possible advantages of interpreting grammars as multiprograms that are susceptible of verification and derivation using the Owicki-Gries logic, a Hoare-based logic from the Multiprogramming field

Optimal, Multi-Modal Control with Applications in Robotics

The objective of this dissertation is to incorporate the concept of optimality to multi-modal control and apply the theoretical results to obtain successful navigation strategies for autonomous mobile robots. The main idea in multi-modal control is to breakup a complex control task into simpler tasks. In particular, number of control modes are constructed, each with respect to a particular task, and these modes are combined according to some supervisory control logic in order to complete the overall control task. This way of modularizing the control task lends itself particularly well to the control of autonomous mobile robot, as evidenced by the success of behavior-based robotics. Many challenging and interesting research issues arise when employing multi-modal control. This thesis aims to address these issues within an optimal control framework. In particular, the contributions of this dissertation are as follows: We first addressed the problem of inferring global behaviors from a collection of local rules (i.e., feedback control laws). Next, we addressed the issue of adaptively varying the multi-modal control system to further improve performance. Inspired by adaptive multi-modal control, we presented a constructivist framework for the learning from example problem. This framework was applied to the DARPA sponsored Learning Applied to Ground Robots (LAGR) project. Next, we addressed the optimal control of multi-modal systems with infinite dimensional constraints. These constraints are formulated as multi-modal, multi-dimensional (M3D) systems, where the dimensions of the state and control spaces change between modes to account for the constraints, to ease the computational burdens associated with traditional methods. Finally, we used multi-modal control strategies to develop effective navigation strategies for autonomous mobile robots. The theoretical results presented in this thesis are verified by conducting simulated experiments using Matlab and actual experiments using the Magellan Pro robot platform and the LAGR robot. In closing, the main strength of multi-modal control lies in breaking up complex control task into simpler tasks. This divide-and-conquer approach helps modularize the control system. This has the same effect on complex control systems that object-oriented programming has for large-scale computer programs, namely it allows greater simplicity, flexibility, and adaptability.Ph.D.Committee Chair: Egerstedt, Magnus; Committee Member: Ferri, Bonnie; Committee Member: Lee, Chin-Hui; Committee Member: Reveliotis, Spyros; Committee Member: Yezzi, Anthon

Maine Alumnus, Volume 17, Number 1, October 1935

Contents: University Opens Sixty-Eighth Year --- Noted Writer [Laura E. Richards] Presented Degree at Home --- Frank Southard \u2710 Heads Maine Legionhttps://digitalcommons.library.umaine.edu/alumni_magazines/1404/thumbnail.jp

Solution sets for equations over free groups are EDT0L languages

© World Scientific Publishing Company. We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constructible EDT0L language. In particular, the set of all solutions in reduced words is an indexed language in the sense of Aho. The language characterization we give, as well as further questions about the existence or finiteness of solutions, follow from our explicit construction of a finite directed graph which encodes all the solutions. Our result incorporates the recently invented recompression technique of Jez, and a new way to integrate solutions of linear Diophantine equations into the process. As a byproduct of our techniques, we improve the complexity from quadratic nondeterministic space in previous works to NSPACE(n log n) here

Models of natural computation : gene assembly and membrane systems

This thesis is concerned with two research areas in natural computing: the computational nature of gene assembly and membrane computing. Gene assembly is a process occurring in unicellular organisms called ciliates. During this process genes are transformed through cut-and-paste operations. We study this process from a theoretical point of view. More specifically, we relate the theory of gene assembly to sorting by reversal, which is another well-known theory of DNA transformation. In this way we obtain a novel graph-theoretical representation that provides new insights into the nature of gene assembly. Membrane computing is a computational model inspired by the functioning of membranes in cells. Membrane systems compute in a parallel fashion by moving objects, through membranes, between compartments. We study the computational power of various classes of membrane systems, and also relate them to other well-known models of computation.Netherlands Organisation for Scientific Research (NWO), Institute for Programming research and Algorithmics (IPA)UBL - phd migration 201

Ogden's lemma for random permitting and forbidding context picture languages and table-driven context-free picture languages

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, February 16, 2015.Random context picture grammars are used to generate pictures through successive refinement. There are three important subclasses of random context picture grammars, namely random permitting context picture grammars, random forbidding context picture grammars and table-driven context-free picture grammars. These grammars generate the random permitting context picture languages, random forbidding context picture languages and table-driven context-free picture languages, respectively. Theorems exist which provide necessary conditions that have to be satisfied by a language before it can be classified under a particular subclass. Some of these theorems include the pumping and shrinking lemmas, which have been developed for random permitting context picture languages and random forbidding context picture languages respectively. Two characterization theorems were developed for the table-driven context-free picture languages. This dissertation examines these existing theorems for picture languages, i.e., the pumping and shrinking lemmas and the two characterisation theorems, and attempts to prove theorems, which will provide an alternative to the existing theorems and thus provide new tools for identifying languages that do not belong to the various classes. This will be done by adapting Ogden’s idea of marking parts of a word which was done for the string case. Our theorems essentially involve marking parts of a picture such that the pumping operation increases the number of marked symbols and the shrinking operation reduces it