Let S be a semigroup, C(S) the automaton constructed from the right Cayley graph of S with respect to all of S as the generating set and ∑(C(S)) the automaton semigroup constructed from C(S). Such semigroups are termed Cayley automaton semigroups. For a given semigroup S we aim to establish connections between S and ∑(C(S)). For a finite monogenic semigroup S with a non-trivial cyclic subgroup C[sub]n we show that ∑(C(S)) is a small extension of a free semigroup of rank n, and that in the case of a trivial subgroup ∑(C(S)) is finite. The notion of invariance is considered and we examine those semigroups S satisfying S ≅ ∑(C(S)). We classify which bands satisfy this, showing that they are those bands with faithful left-regular representations, but exhibit examples outwith this classification. In doing so we answer an open problem of Cain. Following this, we consider iterations of the construction and show that for any n there exists a semigroup where we can iterate the construction n times before reaching a semigroup satisfying S ≅ ∑(C(S)). We also give an example of a semigroup where repeated iteration never produces a semigroup satisfying S ≅ ∑(C(S)). Cayley automaton semigroups of infinite semigroups are also considered and we generalise and extend a result of Silva and Steinberg to cancellative semigroups. We also construct the Cayley automaton semigroup of the bicyclic monoid, showing in particular that it is not finitely generated.

In this study, the regular expressions forming abstract states in Brzozowski’s algorithm are not remapped to sequential state transition table addresses as would be the case in the classical approach, but are hashed to integers. Two regular expressions that are hashed to the same hash code are assigned the same integer address in the state transition table, reducing the number of states in the automaton. This reduction does not necessarily lead to the construction of a minimal automaton: no restrictions are placed on the hash function hashing two regular expressions to the same code. Depending on the quality of the hash function, a super-automaton, previously referred to as an approximate automaton, or an exact automaton can be constructed. When two regular expressions are hashed to the same state, and they do not represent the same regular language, a super-automaton is constructed. A super-automaton accepts the regular language of the input regular expression, in addition to some extra strings. If the hash function is bad, many regular expressions that do not represent the same regular language will be hashed together, resulting in a smaller automaton that accepts extra strings. In the ideal case, two regular expressions will only be hashed together when they represent the same regular language. In this case, an exact minimal automaton will be constructed. It is shown that, using the hashing approach, an exact or super-automaton is always constructed. Another outcome of the hashing approach is that a non-deterministic automaton may be constructed. A new version of the hashing version of Brzozowski’s algorithm is put forward which constructs a deterministic automaton. A method is also put forward for measuring the difference between an exact and a super-automaton: this takes the form of the k-equivalence measure: the k-equivalence measure measures the number of characters up to which the strings of two regular expressions are equal. The better the hash function, the higher the value of k, up to the point where the hash function results in regular expressions being hashed together if and only if they have the same regular language. Using the k-equivalence measure, eight generated hash functions and one hand coded hash function are evaluated for a large number of short regular expressions, which are generated using G¨odel numbers. The k-equivalence concept is extended to the average k-equivalence value in order to evaluate the hash functions for longer regular expressions. The hand coded hash function is found to produce good results. Copyright / Dissertation (MEng)--University of Pretoria, 2009. / Computer Science / unrestricted

This dissertation tracks the automaton’s appearance in Victorian literature from 1840 to 1900. It shows how authors across genre, form, and time conceptualized and responded to the Machine Age, using the automaton as a symbol of humanity’s changing relationship to machine technologies. Chapters 1 and 5 trace how Charlotte Brontë’s Jane Eyre (1847) and E.E. Kellett’s “The New Frankenstein” (1900) similarly address concerns about gender equality in Victorian Britain, challenging the assumption that women could themselves be classified, and controlled, as talking/reproducing automata. Chapter 2 argues that Dickens’s conceptualization of the human machine in Our Mutual Friend (1865) allows his working-class characters a degree of class mobility outside of bourgeois object-oriented ontologies. The automaton informs Dickens’s commentary on Victorian class. Chapter 3 reads The Coming Race (1871) as a reactionary response to what Bulwer-Lytton perceived as the machine’s potential to liberate women from the domestic sphere. In this dystopic vision, women would necessarily come to control all aspects of society when freed of housework by the machine. Chapter 4 looks at Scots working-class poet Alexander Anderson’s 1878 collection Songs of the Rail. Anderson lauds the train engine as savoir and prophet of a coming technological age. I argue that he creates a literary aesthetics for that age by anthropomorphizing the steam engine, extending to it his own poetic voice.

We compare two methods for software specification: <em>algebraic specifications</em> and automata. While algebraic specifications have been around since the 1970s and have been studied extensively, specification by automata is relatively new. Its origins are in another veteran method called <em>trace assertions</em>, which considers a software module as a set of traces, that is, a sequences of function executions. A module is specified by a set of canonical traces and an equivalence relation matching one of the canonical traces to each non-canonical trace. It has been recently shown that trace assertions is an equivalent method to specification by automata. In continuation of this work on trace assertions and automata, we study how automata compare with algebraic specifications. We prove that every specification using an automaton can be converted into an algebraic specification describing the same abstract data type. This conversion utilises a set of canonical words, representing states in the automaton. We next consider varieties of monoids as a heuristic for obtaining more concise algebraic specifications from automata. Finally, we discuss the opposite conversion of algebraic specifications into automata. We show that, while an automaton always exists for every abstract data type described by an algebraic specification, this automaton may not be finitely describable and therefore may not be considered as a viable method for software specification.

There are many existing models of automata working on two-dimensional inputs (pictures), though very little work has been done on the subject of learning of these automata. In this thesis, we introduce a new model called two-dimensional limited context restarting automaton. Our model works similarly as the two-dimensional restarting tiling automaton, yet we show that it is equally powerful as the two-dimensional sgraffito automaton. We propose an algorithm for learning of such automata from positive and negative samples of pictures. The algorithm is implemented and subsequently tested with several basic picture languages. Powered by TCPDF (www.tcpdf.org)

The class of groups generated by automata have been a source of many counterexamples in group theory. At the same time it is connected to other branches of mathematics, such as analysis, holomorphic dynamics, combinatorics, etc. A question that naturally arises is finding the ways to classify these groups. The task of a complete classification and understanding at the moment seems to be too ambitious, but it is reasonable to concentrate on some smaller subclasses of this class. One approach is to consider groups generated by small automata: the automata with k states over d-letter alphabet (so called, (k,d)-automata) with small values of k and d. Certain steps in this directions have been made already: All groups generated by (2,2)-automata have been classified, and groups generated by (3,2)-automata were studied. In this work we study the class of groups generated by (4,2)-automata. More specifically, we partition all such automata into equivalence classes up to symmetry and minimal symmetry (symmetric and minimally symmetric automata naturally generate isomorphic groups) and classify completely all finite groups generated by automata in this class. We also list all classes generating abelian groups. Another important result of the project is developing a database of (4,2)-automata and computational routines that represent a new effective tool for the search for (4,2)-automata generating groups with specific properties, which hopefully will lead to finding counterexamples of certain conjectures.

We compare two methods for software specification: <em>algebraic specifications</em> and automata. While algebraic specifications have been around since the 1970s and have been studied extensively, specification by automata is relatively new. Its origins are in another veteran method called <em>trace assertions</em>, which considers a software module as a set of traces, that is, a sequences of function executions. A module is specified by a set of canonical traces and an equivalence relation matching one of the canonical traces to each non-canonical trace. It has been recently shown that trace assertions is an equivalent method to specification by automata. In continuation of this work on trace assertions and automata, we study how automata compare with algebraic specifications. We prove that every specification using an automaton can be converted into an algebraic specification describing the same abstract data type. This conversion utilises a set of canonical words, representing states in the automaton. We next consider varieties of monoids as a heuristic for obtaining more concise algebraic specifications from automata. Finally, we discuss the opposite conversion of algebraic specifications into automata. We show that, while an automaton always exists for every abstract data type described by an algebraic specification, this automaton may not be finitely describable and therefore may not be considered as a viable method for software specification.

This dissertation presents the development of numerical models based on lattice Boltzmann (LB) and cellular automaton (CA) methods for solving phase change and microstructural evolution problems. First, a new variation of the LB method is discussed for solving the heat conduction problem with phase change. In contrast to previous explicit algorithms, the latent heat source term is treated implicitly in the energy equation, avoiding iteration steps and improving the formulation stability and efficiency. The results showed that the model can deal with phase change problems more accurately and efficiently than explicit LB models. Furthermore, a new numerical technique is introduced for simulating dendrite growth in three dimensions. The LB method is used to calculate the transport phenomena and the CA is employed to capture the solid/liquid interface. It is assumed that the dendritic growth is driven by the difference between the local actual and local equilibrium composition of the liquid in the interface. The evolution of a threedimensional (3D) dendrite is discussed. In addition, the effect of undercooling and degree of anisotropy on the kinetics of dendrite growth is studied. Moreover, effect of melt convection on dendritic solidification is investigated using 3D simulations. It is shown that convection can change the kinetics of growth by affecting the solute distribution around the dendrite. The growth features of twodimensional (2D) and 3D dendrites are compared. Furthermore, the change in growth kinetics and morphology of Al-Cu dendrites is studied by altering melt undercooling, alloy composition and inlet flow velocity. The local-type nature of LB and CA methods enables efficient scaling of the model in petaflops supercomputers, allowing the simulation of large domains in 3D. The model capabilities with large scale simulations of dendritic solidification are discussed and the parallel performance of the algorithm is assessed. Excellent strong scaling up to thousands of computing cores is obtained across the nodes of a computer cluster, along with near-perfect weak scaling. Considering the advantages offered by the presented model, it can be used as a new tool for simulating 3D dendritic solidification under convection.

This thesis focuses on constraints for membership in formal languages under both the systematic search and stochastic local search approaches to constraint programming (CP). Such constraints are very useful in CP for the following three reasons: They provide a powerful tool for user-level extensibility of CP languages. They are very useful for modelling complex work shift regulation constraints, which exist in many shift scheduling problems. In the analysis, testing, and verification of string-manipulating programs, string constraints often arise. We show in this thesis that CP solvers with constraints for membership in formal languages are much more suitable than existing solvers used in tools that have to solve string constraints. In the stochastic local search approach to CP, we make the following two contributions: We introduce a stochastic method of maintaining violations for the regular constraint and extend our method to the automaton constraint with counters. To improve the usage of constraints for which there exists no known constant-time algorithm for neighbour evaluation, we introduce a framework of using solution neighbourhoods, and give an efficient algorithm of constructing a solution neighbourhood for the regular constraint. In the systematic search approach to CP, we make the following two contributions: We show that there may be unwanted consequences when using a propagator that may underestimate a cost of a soft constraint, as the propagator may guide the search to incorrect (non-optimum) solutions to an over-constrained problem. We introduce and compare several propagators that compute correctly the cost of the edit-distance based soft-regular constraint. We show that the context-free grammar constraint is useful and introduce an improved propagator for it.

Depuis plusieurs années, de nombreuses recherches ont été menées autour du diagnostic. Cependant, il est impératif de se préoccuper dès la phase de conception d’un système des objectifs de diagnostic à atteindre. Aussi, de nombreux travaux se sont intéressés à analyser et à caractériser les propriétés de la diagnosticabilité d’un système. La diagnosticabilité est la propriété d’un système garantissant qu’il génère des observations permettant de détecter et discriminer les fautes en temps fini après leur occurrence.Le sujet de cette thèse porte sur les méthodes permettant d’établir les propriétés de la diagnosticabilité des systèmes à événements discrets dans le cadre distribué, sans construction du modèle global du système. Ce cadre est de première importance pour les applications réelles : systèmes naturellement distribués, systèmes trop complexes pour traiter leur modèle global, confidentialité des modèles locaux les uns par rapport aux autres. L’analyse de la diagnosticabilité de tels systèmes distribués se fonde sur des opérations de synchronisation des modèles locaux, par les observations et les communications. D’abord, nous étudions comment optimiser cette analyse de la diagnosticabilité en faisant abstraction de l’information nécessaire et suffisante à partir des objets locaux pour décider la diagnosticabilité globale. L'efficacité de l’algorithme peut être grandement améliorée par la synchronisation des objets locaux et abstraits en comparaison avec celle des objets locaux et non abstraits.Ensuite, nous proposons, dans le cadre distribué, l'algorithme de la diagnosticabilité de motifs d'événements particuliers a priori inobservables dans les systèmes. Ces motifs peuvent être simplement l’occurrence, brutale ou graduelle, d’une faute permanente ou transitoire, plusieurs occurrences d’une faute, plusieurs fautes en cascade, etc. Dans le cadre distribué, la reconnaissance du motif d’événements s’effectue d’abord progressivement dans un sous-système et ensuite la diagnosticabilité de ce motif peut être déterminée par la méthode abstraite et distribuée. Nous prouvons la correction et l'efficacité de notre algorithme à la fois en théorie et en pratique par la mise en œuvre de l’implémentation sur des exemples.Finalement, nous étudions le problème de la diagnosticabilité dans les systèmes distribués avec composants autonomes, où l’information observable est distribuée au lieu d’être centralisée comme jusqu’alors. En d'autres termes, chaque composant ne peut appréhender que ses propres événements observables. Nous donnons la définition de la diagnosticabilité conjointe. Et puis nous discutons de l'indécidabilité de diagnosticabilité conjointe dans le cas général, c'est à dire, les événements de communication ne sont pas observables, avant de proposer un algorithme pour tester sa condition suffisante. De plus, nous obtenons également un résultat de décidabilité et de l'algorithme lorsque les communications sont observables. / Over the latest decades, much research work has been done on automatic fault diagnosis. However, it is imperative to analyze at system design stage how correctness and efficiency and diagnosis algorithm can achieve. Thus many studies were interested in analyzing and characterizing the properties of diagnosability of a system. Diagnosability is the property of a system ensuring that it generates observations for detecting and discriminating faults in finite time after their occurrence.In this thesis, we investigate how to optimize distributed diagnosability analysis by abstracting necessary and sufficient information from local objects to decide global diagnosability decision. The algorithm efficiency can be greatly improved by synchronization of abstracted local objects compared to that of non abstracted local ones.Then we extend the distributed diagnosability algorithm from fault event first to simple pattern and then to general pattern, where pattern can describe more general objects in the diagnosis problem, e.g., multiple faults, multiple occurrences of the same fault, ordered occurrences of significant events, etc. In the distributed framework, the pattern recognition is first incrementally performed normally in a subsystem and then pattern diagnosability can be determined by adjusting abstracted method used in fault event case. We prove the correctness and efficiency of our proposed algorithm both in theory through proof and in practice through implementation.Finally we study joint diagnosability problem in systems with autonomous components, i.e., observable information is distributed instead of centralized. In other words, each component can only observe its own observable events. We give joint diagnosability definition. And then we discuss the undecidability of joint diagnosability in the general case, i.e., communication events are not observable, before proposing an algorithm to test its sufficient condition. In addition, we also get a decidability result and algorithm when communications are observable.