Connected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups

The Automata Processor was designed for string-pattern matching. In this paper, we showcase its use to execute integer and floating-point comparisons and apply the same to accelerate interval stabbing queries. An interval stabbing query determines which of the intervals in a set overlap a query point. Such queries are often used in computational geometry, pattern matching, database management systems, and geographic information systems. The check for each interval is programmed as a single automaton and multiple automata are executed in parallel to provide significant performance gains. While handling 32-bit integers or single-precision floating-point numbers, up to 2.75 trillion comparisons can be executed per second, whereas 0.79 trillion comparisons per second can be completed for 64-bit integers or double-precision floating-point numbers. Additionally, our solution leaves the intervals in the set unordered; allowing addition or deletion of an interval in constant time. This is not possible for contemporary solutions wherein the intervals are ordered, making the query times faster, but making the updating of intervals complex. Our automata designs exemplify techniques that maximize resource utilization and minimize performance bottlenecks, which may be useful to future application developers on this processor. Their modular design allows them to become constituent parts of larger automata, where the numerical comparisons are part of the overall pattern matching operation. We have validated the designs on hardware, and the routines to generate the necessary automata and execute them on the AP will be made available as software libraries shortly.

Cellular automata (CA) are massively parallel systems where a regular grid of finite symbols is updated according to a synchronous application of the same local update rule everywhere. A closely related concept is that of Wang tiles where a local relation between neighboring symbols determines allowed combinations of symbols in the grid. In this tutorial we start with classical results on cellular automata, such as the Garden-of-Eden theorems, the Curtis-Hedlund-Lyndon-theorem and the balance property of surjective cellular automata. We then discuss Wang tiles and, in particular, the concept of aperiodicity and the undecidability of the domino problem. The domino problem is the decision problem to determine if a given Wang tile set admits any valid tilings of the grid. We relate Wang tiles to cellular automata, and establish a number of undecidability results for cellular automata.

An automaton is synchronizing if there exists a word that sends all states of the automaton to a single state. A coloring of a digraph with a fixed out-degree k is a distribution of k labels over the edges resulting in a deterministic finite automaton. The famous road coloring theorem states that every primitive digraph has a synchronizing coloring. We study recent conjectures claiming that the number of synchronizing colorings is large in the worst and average cases. Our approach is based on the spectral properties of the adjacency matrix A(G) of a digraph G. Namely, we study the relation between the number of synchronizing colorings of G and the structure of the dominant eigenvector v of A(G). We show that a vector v has no partition of coordinates into blocks of equal sum if and only if all colorings of the digraphs associated with v are synchronizing. Furthermore, if for each b there exists at most one partition of the coordinates of v into blocks summing up to b, and the total number of partitions is equal to s, then the fraction of synchronizing colorings among all colorings of G is at least (k-s)/k. We also give a combinatorial interpretation of some known results concerning an upper bound on the minimal length of synchronizing words in terms of v.

Efficient pattern matching is fundamental for practical term rewrite engines. By preprocessing the given patterns into a finite deterministic automaton the matching patterns can be decided in a single traversal of the relevant parts of the input term. Most automaton-based techniques are restricted to linear patterns, where each variable occurs at most once, and require an additional post-processing step to check so-called variable consistency. However, we can show that interleaving the variable consistency and pattern matching phases can reduce the number of required steps to find a match all matches. Therefore, we take the existing adaptive pattern matching automata as introduced by Sekar et al and extend it these with consistency checks. We prove that the resulting deterministic pattern matching automaton is correct, and show that its evaluation depth is can be shorter than two-phase approaches.

# Structure of Genetic Regulatory Networks: Evidence for Scale Free Networks (L S Liebovitch et al.) # Modelling Fractal Dynamics (B J West) # Fractional Relaxation of Distributed Order (R Gorenflo & F Mainardi) # Fractional Time: Dishomogeneous Poisson Processes vs. Homogeneous Non-Poisson Processes (P Allegrini et al.) # Markov Memory in Multifractal Natural Processes (N Papasimakis & F Pallikari) # Description of Complex Systems in Terms of Self-Organization Processes of Prime Integer Relations (V Korotkikh & G Korotkikh) # Dynamical Decomposition of Multifractal Time Series as Fractal Evolution and Long-Term Cycles: Applications to Foreign Currency Exchange Market (A Turiel & C Perez-Vicente) # Fractal Sets from Noninvertible Maps (Ch Mira) # A Generative Construction and Visualization of 3D Fractal Measures (T Martyn) # Complexity in Nature and Society: Complexity Management in the Age of Globalization (K Mainzer) # Fractals, Complexity and Chaos in Supply Chain Networks (M Pearson) # The Effects of Different Competition Rules on the Power-Law Exponent of High Income Distribution (K Yamamoto et al.) # Synergetics on Its Way to the Life Sciences (H Haken) # Complexity, Fractals, Nature and Industrial Design: Some Connections (N Sala) # Modelling Pattern Formation Upon Laser-Induced Etching (A Mora et al.) # Fractal Properties of Some Machined Surfaces (T R Thomas & B-G Rosen) # Fractals, Morphological Spectrum and Complexity of Interfacial Patterns in Non-Equilibrium Solidification (P K Galenko & D M Herlach) # Competition of Doublon Structure in the Phase-Field Model (S Tokunaga & H Sakaguchi) # Study of Thermal Field in Composite Materials (P Stefkova et al.) # Simulation of Geochemical Banding in Acidization-Precipitation Experiments In Situ (M Msharrafieh et al.) # Bulk Mediated Surface Diffusion: Non Markovian and Biased Behavior (J A Revelli et al) # Multifractal Formalism for Remote Sensing: A Contribution to the Description and the Understanding of Meteorological Phenomena in Satellite Images (J Grazzini et al.) # The Distance Ratio Fractal Image (X-Z Zhang et al.) # Iterated Function Systems in Mixed Euclidean and p-Adic Spaces (B Sing) # Multifractality of the Multiplicative Autogressive Point Processes (B Kaulakys et al.) # Analysis of Geographical Distribution Patterns in Plants Using Fractals (A Bari et al.) # Hierarchy of Cellular Automata in Relation to Control of Chaos or Anticontrol (M Markus et al.) # Fractal Analysis of the Images Using Wavelet Transformation (P Jerabkova et al.) # Clustering Phenomena in the Time Distribution of Lightning (L Telesca et al.) # A Cornucopia of Connections: Finding Four Familiar Fractals in the Tower of Hanoi (D R Camp) # Monitoring the Depth of Anaesthesia Using Fractal Complexity Method (W Klonowski et al.) # The Complex Couplings and Gompertzian Dynamics (P Waliszewski & J Konarski)

This paper shows an educational software for evaluation of Formal Languages subject. Along with a simple interface of easy understanding and application, it is going to present exercises where the student will visualize the automaton on 3D and shall develop the ‘regular expression’ and in a second moment shall develop a minimization of the automaton interacting directly to the 3D object. For the drawing of the automatons, the software uses tools in 3D, how Blender and the VRML and for the edition of the page on the internet along with proposed exercises the programming language PHP is used. After the accomplishment of the proposed exercises the student will send automatically the answers and the final result of the evaluation for his/her e-mail and to the teacher´s e-mail, making thus the evaluation fast and efficient. This software intends to take the subject in referral from the classroom to the informatics labs and will become more appealing to the student, rendering easier the evaluation. Key words: Formal languages, regular expression, 3D, automat, blender, virtual reality modeling language, hypertext prepocessor (PHP)

In this article, we develop a new and somewhat unexpected connection between higher-order model-checking and linear logic. Our starting point is the observation that once embedded in the relational semantics of linear logic, the Church encoding of any higher-order recursion scheme (HORS) comes together with a dual Church encoding of an alternating tree automata (ATA) of the same signature. Moreover, the interaction between the relational interpretations of the HORS and of the ATA identifies the set of accepting states of the tree automaton against the infinite tree generated by the recursion scheme. We show how to extend this result to alternating parity automata (APT) by introducing a parametric version of the exponential modality of linear logic, capturing the formal properties of colors (or priorities) in higher-order model-checking. We show in particular how to reunderstand in this way the type-theoretic approach to higher-order model-checking developed by Kobayashi and Ong. We briefly explain in the end of the paper how this analysis driven by linear logic results in a new and purely semantic proof of decidability of the formulas of the monadic second-order logic for higher-order recursion schemes.

Groups and semigroups generated by Mealy automata were formally introduced in the early 1960s. They revealed their full potential over the years, by contributing to important conjectures in group theory. In the current chapter, we intend to provide various combinatorial and dynamical tools to tackle some decision problems all related to some extent to the growth of automaton (semi)groups. In the first part, we consider Wang tilings as a major tool in order to study and understand the behavior of automaton (semi)groups. There are various ways to associate a Wang tileset with a given complete and deterministic Mealy automaton and various ways to interpret the induced Wang tilings. We describe some of these fruitful combinations, as well as some promising research opportunities. In the second part, we detail some toggle switch between a classical notion from group theory—Schreier graphs—and some properties of an automaton group about its growth or the growth of its monogenic subgroups. We focus on polynomial-activity automata and on reversible automata, which are somehow diametrically opposed families.

The elliptic curve cryptography is almost used in the literature to develop the public key cryptosystems. A new general-purpose symmetric key cryptosystem using elliptic prime curves is proposed in this paper. For a given prime number P, there are many elliptic prime curves on which each point in the quadrant (0,0) to (P-1,P-1) lays. The set of minimum number of eligible elliptic prime curves for a given prime number P constitutes a lookup table that is the secret key of the proposed cryptosystem. The sender can pick up one eligible elliptic curve for each 2n-bit plaintext block. The sender sends two integers cipher for each 2n-bit plaintext block with encryption rate = 0.8. Moreover, a small prime number can be used efficiently with high security and good robustness against brute force attack.

We show that several problems concerning probabilistic finite automata of a fixed dimension and a fixed number of letters for bounded cut-point and strict cut-point languages are algorithmically un...

CELLULAR AUTOMATA MODELLING APPROACH FOR URBAN GROWTH

We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective characterizations of ftw-NFAs and a tight worst-case state size bound for determinizing an ftw-NFA $A$ as a function of the tree width and the number of states of $A$. We also introduce a lower bound technique for ftw-NFAs.

This paper describes an innovative approach to network testing based on automatically generating and analyzing state machine models of network behavior. The models are generated by the network test tool AGATE (Automatic Generator of Automata for TEsting), which is also described in this paper. The proposed test approach mimics experimental method, requiring repeated cycles of observing the network, modeling the network, making predictions about network behavior, and evaluating predictions. This paper focusses on the modeling step, in which the test tool AGATE automatically generates representative state machines from observed network traces. The generated state machines closely approximate the behavior of components of the network under test. Faults in the system may be immediately apparent from the state machines, but more importantly the state machines can be used for formal analysis. We propose this as a cost-effective alternative to manually defining a state machine before beginning tests.

Essentially, in a reversible programming language, for each forward computation step from state S to state S', there exists a constructive and deterministic method to go backwards from state S' to state S. Besides its theoretical interest, reversible computation is a fundamental concept which is relevant in many different areas like cellular automata, bidirectional program transformation, or quantum computing, to name a few. In this paper, we focus on term rewriting, a computation model that underlies most rule-based programming languages. In general, term rewriting is not reversible, even for injective functions; namely, given a rewrite step t1 -> t2, we do not always have a decidable and deterministic method to get t1 from t2. Here, we introduce a conservative extension of term rewriting that becomes reversible. Furthermore, we also define a transformation to make a rewrite system reversible using standard term rewriting.

Bone remodeling is the biological process through which old bone tissue is transformed into new bone through the action of a basic unit of bone remodeling (BMU). This paper presents a computational model to determine the variation of cell population caused by the presence of micro-fractures within the BMU during the remodeling process, also determines the spatial evolution at particular points of the trabecular bone surface. The remodeling process presented is governed by a twodimensional cellular automaton that evolves according to a set of rules and states, based on biological processes that occur in bone remodeling. The simulation of the remodeling process, programmed in MATLAB® performed in time intervals of 0.3 seconds, in the model showed a ratio of 20 osteoclasts to 190 osteoblasts. On the other hand, an approximate resorption time of 34 days and 150 days for formation was obtained. Bone mass showed a maximum percentage loss of 19%.