Counter Machines and Distributed Automata: A Story about Exchanging Space and Time

We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of counters. The two classes differ in the extra features they offer: one allows to copy counter values, whereas the other allows to compute copyless sums of counters. Our distributed automata, on the other hand, operate on directed path graphs that represent words. All nodes of a path synchronously execute the same finite-state machine, whose state diagram must be acyclic except for self-loops, and each node receives as input the state of its direct predecessor. These devices form a subclass of linear-time one-way cellular automata.Comment: 15 pages (+ 13 pages of appendices), 5 figures; To appear in the proceedings of AUTOMATA 2018

Complexity of Two-Dimensional Patterns

In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of ``regular language'' or ``local rule'' that are equivalent in d=1 lead to distinct classes in d >= 2. We explore the closure properties and computational complexity of these classes, including undecidability and L-, NL- and NP-completeness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in d >= 2 has a periodic point of a given period, and that certain ``local lattice languages'' are not finite-time images or limit sets of any CA. We also show that the entropy of a d-dimensional CA's finite-time image cannot decrease faster than t^{-d} unless it maps every initial condition to a single homogeneous state.Comment: To appear in J. Stat. Phy

REGULAR LANGUAGES: TO FINITE AUTOMATA AND BEYOND - SUCCINCT DESCRIPTIONS AND OPTIMAL SIMULATIONS

\uc8 noto che i linguaggi regolari \u2014 o di tipo 3 \u2014 sono equivalenti agli automi a stati finiti. Tuttavia, in letteratura sono presenti altre caratterizzazioni di questa classe di linguaggi, in termini di modelli riconoscitori e grammatiche. Per esempio, limitando le risorse computazionali di modelli pi\uf9 generali, quali grammatiche context-free, automi a pila e macchine di Turing, che caratterizzano classi di linguaggi pi\uf9 ampie, \ue8 possibile ottenere modelli che generano o riconoscono solamente i linguaggi regolari. I dispositivi risultanti forniscono delle rappresentazioni alternative dei linguaggi di tipo 3, che, in alcuni casi, risultano significativamente pi\uf9 compatte rispetto a quelle dei modelli che caratterizzano la stessa classe di linguaggi. Il presente lavoro ha l\u2019obiettivo di studiare questi modelli formali dal punto di vista della complessit\ue0 descrizionale, o, in altre parole, di analizzare le relazioni tra le loro dimensioni, ossia il numero di simboli utilizzati per specificare la loro descrizione. Sono presentati, inoltre, alcuni risultati connessi allo studio della famosa domanda tuttora aperta posta da Sakoda e Sipser nel 1978, inerente al costo, in termini di numero di stati, per l\u2019eliminazione del nondeterminismo dagli automi stati finiti sfruttando la capacit\ue0 degli automi two-way deterministici di muovere la testina avanti e indietro sul nastro di input.It is well known that regular \u2014 or type 3 \u2014 languages are equivalent to finite automata. Nevertheless, many other characterizations of this class of languages in terms of computational devices and generative models are present in the literature. For example, by suitably restricting more general models such as context-free grammars, pushdown automata, and Turing machines, that characterize wider classes of languages, it is possible to obtain formal models that generate or recognize regular languages only. The resulting formalisms provide alternative representations of type 3 languages that may be significantly more concise than other models that share the same expressing power. The goal of this work is to investigate these formal systems from a descriptional complexity perspective, or, in other words, to study the relationships between their sizes, namely the number of symbols used to write down their descriptions. We also present some results related to the investigation of the famous question posed by Sakoda and Sipser in 1978, concerning the size blowups from nondeterministic finite automata to two-way deterministic finite automata

Object-oriented engineering of visual languages

Visual languages are notations that employ graphics (icons, diagrams) to present information in a two or more dimensional space. This work focuses on diagrammatic visual languages, as found in software engineering, and their computer implementations. Implementation means the development of processors to automatically analyze diagrams and the development of graphical editors for constructing the diagrams. We propose a rigorous implementation technique that uses a formal grammar to specify the syntax of a visual language and that uses parsing to automatically analyze the visual sentences generated by the grammar. The theoretical contributions of our work are an original treatment of error handling (error detection, reporting, and recovery) in off-line visual language parsing, and the source-to-source translation of visual languages. We have also substantially extended an existing grammatical model for multidimensional languages, called atomic relational grammars. We have added support for meta-language expressions that denote optional and repetitive right-hand-side elements. We hav

Combining SOA and BPM Technologies for Cross-System Process Automation

This paper summarizes the results of an industry case study that introduced a cross-system business process automation solution based on a combination of SOA and BPM standard technologies (i.e., BPMN, BPEL, WSDL). Besides discussing major weaknesses of the existing, custom-built, solution and comparing them against experiences with the developed prototype, the paper presents a course of action for transforming the current solution into the proposed solution. This includes a general approach, consisting of four distinct steps, as well as specific action items that are to be performed for every step. The discussion also covers language and tool support and challenges arising from the transformation

Binding Phenomena Within A Reductionist Theory of Grammatical Dependencies

This thesis investigates the implications of binding phenomena for the development of a reductionist theory of grammatical dependencies. The starting point is the analysis of binding and control in Hornstein (2001, 2009). A number of revisions are made to this framework in order to develop a simpler and empirically more successful account of binding phenomena. The major development is the rejection of economy-based accounts of Condition B effects. It is argued that Condition B effects derive directly from an anti-locality constraint on A-movement. Competition between different dependency types is crucial to the analysis, but is formulated in terms of a heavily revised version of Reinhart's (2006) "No Sneaking" principle, rather than in terms of a simple economy preference for local over non-local dependencies. In contrast to Reinhart's No Sneaking, the condition presented here ("Keeping Up Appearances") has a phonologically rather than semantically specified comparison set. A key claim of the thesis is that the morphology of pronouns and reflexives is of little direct grammatical import. It is argued that much of the complexity of the contemporary binding literature derives from the attempt to capture the distribution of pronouns and reflexives in largely, or purely, syntactic and semantic terms. The analysis presented in this dissertation assigns a larger role to language-specific "spellout" rules, and to general pragmatic/interpretative principles governing the choice between competing morphemes. Thus, a core assumption of binding theory from LGB onwards is rejected: there is no syntactic theory which accounts for the distribution of pronouns and reflexives. Rather, there is a core theory of grammatical dependencies which must be conjoined with with phonological, morphological and pragmatic principles to yield the distributional facts in any given language. In this respect, the approach of the thesis is strictly non-lexicalist: there are no special lexical items which trigger certain kinds of grammatical dependency. All non-strictly-local grammatical dependencies are formed via A- or A-chains, and copies in these chains are pronounced according to a mix of universal principles and language-specific rules. The broader goal of the thesis is to further the prospects for a "reductionist" approach to grammatical dependencies along these lines. The most detailed empirical component of the thesis is an investigation of the problem posed by binding out of prepositional phrases. Even in a framework incorporating sideward movement, the apparent lack of c-command in this configuration poses a problem. Chapter 3 attempts to revive a variant of the traditional "reanalysis" account of binding out of PP. This segues into an investigation of certain properties of pseudopassivization and preposition stranding. The analyses in this thesis are stated within an informal syntactic framework. However, in order to investigate the precise implications of a particular economy condition, Merge over Move, a partial formalization of this framework is developed in chapter 4. This permits the economy condition to be stated precisely, and in a manner which does not have adverse implications for computational complexity