On the Gap-Complexity of Simple RL-Automata

Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. All types of restarting automata considered in the literature up to now accept at least the deterministic context-free languages. Here we introduce and study a new type of restarting automaton, the so-called t-RL-automaton, which is an RL-automaton that is rather restricted in that it has a window of size one only, and that it works under a minimal acceptance condition. On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle. Here we study the gap-complexity of these automata. The membership problem for a language that is accepted by a t-RL-automaton with a bounded number of gaps can be solved in polynomial time. On the other hand, t-RL-automata with an unbounded number of gaps accept NP-complete languages.

On the Descriptional Complexity of Simple RL-Automata

Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. Here we study a new type of restarting automaton, the so-called t-sRL-automaton, which is an RL-automaton that is rather restricted in that it has a window of size 1 only, and that it works under a minimal acceptance condition. On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle. We focus on the descriptional complexity of these automata, establishing two complexity measures that are both based on the description of t-sRL-automata in terms of so-called meta-instructions. We present some hierarchy results as well as a non-recursive trade-off between deterministic 2-sRL-automata and finite-state acceptors.

On Alternating Non-Context-Free Grammars

We study several extensions of the notion of alternation from context-free grammars to context-sensitive and arbitrary phrase-structure grammars. Thereby new grammatical characterizations are obtained for the class of languages that are accepted by alternating pushdown automata.

The Degree of Word-Expansion of Lexicalized RRWW-Automata

Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based on the number of auxiliary symbols (categories) used for recognizing a language as the projection of its characteristic language onto its input alphabet. This type of recognition is typical for analysis by reduction, a method used in linguistics for the creation and verification of formal descriptions of natural languages. Our main results establish a hierarchy of classes of context-free languages and two hierarchies of classes of non-context-free languages that are based on the expansion factor of a language.

CD-Systems of Restarting Automata

Die vorliegende Arbeit behandelt Restartautomaten und Erweiterungen von Restartautomaten. Restartautomaten sind ein Werkzeug zum Erkennen formaler Sprachen. Sie sind motiviert durch die linguistische Methode der Analyse durch Reduktion und wurden 1995 von Jancar, Mráz, Plátek und Vogel eingeführt. Restartautomaten bestehen aus einer endlichen Kontrolle, einem Lese/Schreibfenster fester Größe und einem flexiblen Band. Anfänglich enthält dieses sowohl die Eingabe als auch Bandbegrenzungssymbole. Die Berechnung eines Restartautomaten läuft in so genannten Zyklen ab. Diese beginnen am linken Rand im Startzustand, in ihnen wird eine lokale Ersetzung auf dem Band durchgeführt und sie enden mit einem Neustart, bei dem das Lese/Schreibfenster wieder an den linken Rand bewegt wird und der Startzustand wieder eingenommen wird. Die vorliegende Arbeit beschäftigt sich hauptsächlich mit zwei Erweiterungen der Restartautomaten: CD-Systeme von Restartautomaten und nichtvergessende Restartautomaten. Nichtvergessende Restartautomaten können einen Zyklus in einem beliebigen Zustand beenden und CD-Systeme von Restartautomaten bestehen aus einer Menge von Restartautomaten, die zusammen die Eingabe verarbeiten. Dabei wird ihre Zusammenarbeit durch einen Operationsmodus, ähnlich wie bei CD-Grammatik Systemen, geregelt. Für beide Erweiterungen zeigt sich, dass die deterministischen Modelle mächtiger sind als deterministische Standardrestartautomaten. Es wird gezeigt, dass CD-Systeme von Restartautomaten in vielen Fällen durch nichtvergessende Restartautomaten simuliert werden können und andererseits lassen sich auch nichtvergessende Restartautomaten durch CD-Systeme von Restartautomaten simulieren. Des Weiteren werden Restartautomaten und nichtvergessende Restartautomaten untersucht, die nichtdeterministisch sind, aber keine Fehler machen. Es zeigt sich, dass diese Automaten durch deterministische (nichtvergessende) Restartautomaten simuliert werden können, wenn sie direkt nach der Ersetzung einen neuen Zyklus beginnen, oder ihr Fenster nach links und rechts bewegen können. Außerdem gilt, dass alle (nichtvergessenden) Restartautomaten, die zwar Fehler machen dürfen, diese aber nach endlich vielen Zyklen erkennen, durch (nichtvergessende) Restartautomaten simuliert werden können, die keine Fehler machen. Ein weiteres wichtiges Resultat besagt, dass die deterministischen monotonen nichtvergessenden Restartautomaten mit Hilfssymbolen, die direkt nach dem Ersetzungsschritt den Zyklus beenden, genau die deterministischen kontextfreien Sprachen erkennen, wohingegen die deterministischen monotonen nichtvergessenden Restartautomaten mit Hilfssymbolen ohne diese Einschränkung echt mehr, nämlich die links-rechts regulären Sprachen, erkennen. Damit werden zum ersten Mal Restartautomaten mit Hilfssymbolen, die direkt nach dem Ersetzungsschritt ihren Zyklus beenden, von Restartautomaten desselben Typs ohne diese Einschränkung getrennt. Besonders erwähnenswert ist hierbei, dass beide Automatentypen wohlbekannte Sprachklassen beschreiben.

Lower Bounds for Nonforgetting Restarting Automata and CD-Systems of Restarting Automata

The nonforgetting restarting automaton is a generalization of the restarting automaton that, when executing a restart operation, changes its internal state based on the current state and the actual contents of its read/write window instead of resetting it to the initial state. Another generalization of the restarting automaton is the cooperating distributed system (CD-system) of restarting automata. Here a finite system of restarting automata works together in analyzing a given sentence, where they interact based on a given mode of operation. As it turned out, CD-systems of restarting automata of some type X working in mode =1 are just as expressive as nonforgetting restarting automata of the same type X. Further, various types of determinism have been introduced for CD-systems of restarting automata called strict determinism, global determinism, and local determinism, and it has been shown that globally deterministic CD-systems working in mode =1 correspond to deterministic nonforgetting restarting automata. Here we derive some lower bound results for some types of nonforgetting restarting automata and for some types of CD-systems of restarting automata. In this way we establish separations between the corresponding language classes, thus providing detailed technical proofs for some of the separation results announced in the literature.

On Parallel Communicating Grammar Systems and Correctness Preserving Restarting Automata

This paper contributes to the study of Freely Rewriting Restarting Automata (FRR-automata) and Parallel Communicating Grammar Systems (PCGS), which both are useful models in computational linguistics. For PCGSs we study two complexity measures called 'generation complexity' and 'distribution complexity', and we prove that a PCGS Pi, for which the generation complexity and the distribution complexity are both bounded by constants, can be transformed into a freely rewriting restarting automaton of a very restricted form. From this characterization it follows that the language L(Pi) generated by Pi is semi-linear, that its characteristic analysis is of polynomial size, and that this analysis can be computed in polynomial time.

CD-Systems of Restarting Automata Governed by Explicit Enable and Disable Conditions

We introduce a new mode of operation for CD-systems of restarting automata by providing explicit enable and disable conditions in the form of regular constraints. We show that, for each CD-system M of restarting automata and each mode m of operation considered by Messerschmidt and Otto, there exists a CD-system M' of restarting automata of the same type as M that, working in the new mode ed, accepts the language that M accepts in mode m. Further, we prove that in mode ed, a locally deterministic CD-system of restarting automata of type RR(W)(W) can be simulated by a locally deterministic CD-system of restarting automata of the more restricted type R(W)(W). This is the first time that a non-monotone type of R-automaton without auxiliary symbols is shown to be as expressive as the corresponding type of RR-automaton.

On CD-systems of stateless deterministic R-automata with window size one

We study cooperating distributed systems (CD-systems) of restarting automata that are very restricted: they are deterministic, they cannot rewrite, but only delete symbols, they restart immediately after performing a delete operation, they are stateless, and they have a read/write window of size 1 only, that is, these are stateless deterministic R(1)-automata. We study the expressive power of these systems by relating the class of languages that they accept by mode =1 computations to other well-studied language classes, showing in particular that this class only contains semi-linear languages, and that it includes all rational trace languages. In addition, we investigate the closure and non-closure properties of this class of languages and some of its algorithmic properties.

CD-Systems of Stateless Deterministic R(1)-Automata Governed by an External Pushdown Store

We study cooperating distributed systems (CD-systems) of stateless deterministic restarting automata with window size 1 that are governed by an external pushdown store. In this way we obtain an automata-theoretical characterization for the class of context-free trace languages.

On Globally Deterministic CD-Systems of Stateless R-Automata with Window Size One

It is known that cooperating distributed systems (CD-systems) of stateless deterministic restarting automata with window size 1 accept a class of semi-linear languages that properly includes all rational trace languages. Although the component automata of such a CD-system are all deterministic, in general the CD-system itself is not, as in each of its computations, the initial component and the successor components are still chosen nondeterministically. Here we study CD-systems of stateless deterministic restarting automata with window size 1 that are themselves completely deterministic. In fact, we consider two such types of CD-systems, the strictly deterministic systems and the globally deterministic systems.

Relations and Transductions Realized by Restarting Automata

Gegenstand der vorliegenden Arbeit ist die Analyse verschiedener Formalismen zur Berechnung binärer Wortrelationen. Dabei ist die Grundlage aller hier ausgeführten Betrachtungen das Modell der Restart-Automaten, welches 1995 von Jancar et. al. eingeführt wurde. Zum einen wird das bereits für Restart-Automaten bekannte Konzept der input/output- und proper-Relationen weiterführend untersucht, sowie auf Systeme von zwei parallel arbeitenden und miteinander kommunizierenden Restart-Automaten (PC-Systeme) erweitert. Zum anderen wird eine Variante der Restart-Automaten eingeführt, die sich an klassischen Automatenmodellen zur Berechnung von Relationen orientiert. Mit Hilfe dieser Mechanismen kann gezeigt werden, dass einige Klassen, die durch input/output- und proper-Relationen von Restart Automaten definiert werden, mit den traditionellen Relationsklassen der Rationalen Relationen und der Pushdown-Relationen übereinstimmen. Weiterhin stellt sich heraus, dass das Konzept der parallel kommunizierenden Automaten äußerst mächtig ist, da bereits die Klasse der proper-Relationen von monotonen PC-Systemen alle berechenbaren Relationen umfasst. Der Haupteil der Arbeit beschäftigt sich mit den so genannten Restart-Transducern, welche um eine Ausgabefunktion erweiterte Restart-Automaten sind. Es zeigt sich, dass sich insbesondere dieses Modell mit seinen verschiedenen Erweiterungen und Einschränkungen dazu eignet, eine umfassende Hierarchie von Relationsklassen zu etablieren. In erster Linie seien hier die verschiedenen Typen von monotonen Restart-Transducern erwähnt, mit deren Hilfe viele interessante neue und bekannte Relationsklassen innerhalb der längenbeschränkten Pushdown-Relationen charakterisiert werden. Abschließend wird, im Kontrast zu den vorhergehenden Modellen, das nicht auf Restart-Automaten basierende Konzept des Übersetzens durch Beobachtung ("Transducing by Observing") zur Relationsberechnung eingeführt. Dieser, den Restart-Transducern nicht unähnliche Mechanismus, wird im weitesten Sinne dazu genutzt, einen anderen Blickwinkel auf die von Restart-Transducern definierten Relationen einzunehmen, sowie eine obere Schranke für die Berechnungskraft der Restart-Transducer zu gewinnen.

Path planning of robots in noisy workspaces using learning automata

The problem of a manipulator operating in a noisy workspace and required to move from an initial fixed position P0 to a final position Pf is considered. However, Pf is corrupted by noise, giving rise to Pˆf, which may be obtained by sensors. The use of learning automata is proposed to tackle this problem. An automaton is placed at each joint of the manipulator which moves according to the action chosen by the automaton (forward, backward, stationary) at each instant. The simultaneous reward or penalty of the automata enables avoiding any inverse kinematics computations that would be necessary if the distance of each joint from the final position had to be calculated. Three variable-structure learning algorithms are used, i.e., the discretized linear reward-penalty (DLR-P, the linear reward-penalty (LR-P ) and a nonlinear scheme. Each algorithm is separately tested with two (forward, backward) and three forward, backward, stationary) actions.

Trajectory planning of a robot using learning algorithms

The authors consider the problem of a robot manipulator operating in a noisy workspace. The manipulator is required to move from an initial position P(i) to a final position P(f). P(i) is assumed to be completely defined. However, P(f) is obtained by a sensing operation and is assumed to be fixed but unknown. The authors approach to this problem involves the use of three learning algorithms, the discretized linear reward-penalty (DLR-P) automaton, the linear reward-penalty (LR-P) automaton and a nonlinear reinforcement scheme. An automaton is placed at each joint of the robot and by acting as a decision maker, plans the trajectory based on noisy measurements of P(f).

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.