A Minimal Time Solution to the Firing Squad Synchronization Problem with Von Neumann Neighborhood of Extent 2

Cellular automata provide a simple environment in which to study global behaviors. One example of a problem that utilizes cellular automata is the Firing Squad Synchronization Problem, first proposed in 1957. This paper provides an overview of the standard Firing Squad Synchronization Problem and a commonly used technique in solving it. This paper also provides a statement of a new extension of the Standard Firing Squad Synchronization Problem to a different neighborhood definition - a Von Neumann neighborhood of extent 2. An 8 state 651 rule minimal time solution to the extended problem is described, presented and proven, along with Python code used in running simulations of the solution

MFCS\u2798 Satellite Workshop on Cellular Automata

For the 1998 conference on Mathematical Foundations of Computer Science (MFCS\u2798) four papers on Cellular Automata were accepted as regular MFCS\u2798 contributions. Furthermore an MFCS\u2798 satellite workshop on Cellular Automata was organized with ten additional talks. The embedding of the workshop into the conference with its participants coming from a broad spectrum of fields of work lead to interesting discussions and a fruitful exchange of ideas. The contributions which had been accepted for MFCS\u2798 itself may be found in the conference proceedings, edited by L. Brim, J. Gruska and J. Zlatuska, Springer LNCS 1450. All other (invited and regular) papers of the workshop are contained in this technical report. (One paper, for which no postscript file of the full paper is available, is only included in the printed version of the report). Contents: F. Blanchard, E. Formenti, P. Kurka: Cellular automata in the Cantor, Besicovitch and Weyl Spaces K. Kobayashi: On Time Optimal Solutions of the Two-Dimensional Firing Squad Synchronization Problem L. Margara: Topological Mixing and Denseness of Periodic Orbits for Linear Cellular Automata over Z_m B. Martin: A Geometrical Hierarchy of Graph via Cellular Automata K. Morita, K. Imai: Number-Conserving Reversible Cellular Automata and Their Computation-Universality C. Nichitiu, E. Remila: Simulations of graph automata K. Svozil: Is the world a machine? H. Umeo: Cellular Algorithms with 1-bit Inter-Cell Communications F. Reischle, Th. Worsch: Simulations between alternating CA, alternating TM and circuit families K. Sutner: Computation Theory of Cellular Automat

Parallel turing machines with one-head control units and cellular automata

Parallel Turing machines (PTM) can be viewed as a generalization of cellular automata (CA) where an additional measure called processor complexity can be defined which indicates the ``amount of parallelism\u27\u27 used. In this paper PTM are investigated with respect to their power as recognizers of formal languages. A combinatorial approach as well as diagonalization are used to obtain hierarchies of complexity classes for PTM and CA. In some cases it is possible to keep the space complexity of PTM fixed. Thus for the first time it is possible to find hierarchies of complexity classes (though not CA classes) which are completely contained in the class of languages recognizable by CA with space complexity n and in polynomial time. A possible collapse of the time hierarchy for these CA would therefore also imply some unexpected properties of PTM

Pattern formations with discrete waves and broadcasting sequences

This thesis defines the Broadcasting Automata model as an intuitive and complete method of distributed pattern formation, partitioning and distributed geometric computation. The system is examined within the context of Swarm Robotics whereby large numbers of minimally complex robots may be deployed in a variety of circumstances and settings with goals as diverse as from toxic spill containment to geological survey. Accomplishing these tasks with such simplistic machines is complex and has been deconstructed in to sub-problems considered to be signif- icant because, when composed, they are able to solve much more complex tasks. Sub-problems have been identified, and studied as pattern formation, leader elec- tion, aggregation, chain formation, hole avoidance, foraging, path formation, etc. The Broadcasting Automata draws inspiration from a variety of sources such as Ad-Hoc radio networks, cellular automata, neighbourhood sequences and nature, employing many of the same pattern forming methods that can be seen in the superposition of waves and resonance. To this end the thesis gives an in depth analysis of the primitive tools of the Broadcasting Automata model, nodal patterns, where waves from a variety of transmitters can in linear time construct partitions and patterns with results per- taining to the numbers of different patterns and partitions, along with the number of those that differ, are given. Using these primitives of the model a variety of algorithms are given including leader election, through the location of the centre of a discrete disc, and a solution to the Firing Squad Synchronisation problem. These problems are solved linearly.An exploration of the ability to vary the broadcasting radius of each node leads to results of categorisations of digital discs, their form, composition, encodings and generation. Results pertaining to the nodal patterns generated by arbitrary transmission radii on the plane are explored with a connection to broadcasting sequences and approximation of discrete metrics of which results are given for the approximation of astroids, a previously unachievable concave metric, through a novel application of the aggregation of waves via a number of explored functions. Broadcasting Automata aims to place itself as a robust and complete linear time and large scale system for the construction of patterns, partitions and geometric computation. Algorithms and methodologies are given for the solution of problems within Swarm Robotics and an extension to neighbourhood sequences. It is also hoped that it opens up a new area of research that can expand many older and more mature works

A Language-centered Approach to support environmental modeling with Cellular Automata

Die Anwendung von Methodiken und Technologien aus dem Bereich der Softwaretechnik auf den Bereich der Umweltmodellierung ist eine gemeinhin akzeptierte Vorgehensweise. Im Rahmen der "modellgetriebenen Entwicklung"(MDE, model-driven engineering) werden Technologien entwickelt, die darauf abzielen, Softwaresysteme vorwiegend auf Basis von im Vergleich zu Programmquelltexten relativ abstrakten Modellen zu entwickeln. Ein wesentlicher Bestandteil von MDE sind Techniken zur effizienten Entwicklung von "domänenspezifischen Sprachen"( DSL, domain-specific language), die auf Sprachmetamodellen beruhen. Die vorliegende Arbeit zeigt, wie modellgetriebene Entwicklung, und insbesondere die metamodellbasierte Beschreibung von DSLs, darüber hinaus Aspekte der Pragmatik unterstützen kann, deren Relevanz im erkenntnistheoretischen und kognitiven Hintergrund wissenschaftlichen Forschens begründet wird. Hierzu wird vor dem Hintergrund der Erkenntnisse des "modellbasierten Forschens"(model-based science und model-based reasoning) gezeigt, wie insbesondere durch Metamodelle beschriebene DSLs Möglichkeiten bieten, entsprechende pragmatische Aspekte besonders zu berücksichtigen, indem sie als Werkzeug zur Erkenntnisgewinnung aufgefasst werden. Dies ist v.a. im Kontext großer Unsicherheiten, wie sie für weite Teile der Umweltmodellierung charakterisierend sind, von grundsätzlicher Bedeutung. Die Formulierung eines sprachzentrierten Ansatzes (LCA, language-centered approach) für die Werkzeugunterstützung konkretisiert die genannten Aspekte und bildet die Basis für eine beispielhafte Implementierung eines Werkzeuges mit einer DSL für die Beschreibung von Zellulären Automaten (ZA) für die Umweltmodellierung. Anwendungsfälle belegen die Verwendbarkeit von ECAL und der entsprechenden metamodellbasierten Werkzeugimplementierung.The application of methods and technologies of software engineering to environmental modeling and simulation (EMS) is common, since both areas share basic issues of software development and digital simulation. Recent developments within the context of "Model-driven Engineering" (MDE) aim at supporting the development of software systems at the base of relatively abstract models as opposed to programming language code. A basic ingredient of MDE is the development of methods that allow the efficient development of "domain-specific languages" (DSL), in particular at the base of language metamodels. This thesis shows how MDE and language metamodeling in particular, may support pragmatic aspects that reflect epistemic and cognitive aspects of scientific investigations. For this, DSLs and language metamodeling in particular are set into the context of "model-based science" and "model-based reasoning". It is shown that the specific properties of metamodel-based DSLs may be used to support those properties, in particular transparency, which are of particular relevance against the background of uncertainty, that is a characterizing property of EMS. The findings are the base for the formulation of an corresponding specific metamodel- based approach for the provision of modeling tools for EMS (Language-centered Approach, LCA), which has been implemented (modeling tool ECA-EMS), including a new DSL for CA modeling for EMS (ECAL). At the base of this implementation, the applicability of this approach is shown

CACIC 2015 : XXI Congreso Argentino de Ciencias de la Computación. Libro de actas

Actas del XXI Congreso Argentino de Ciencias de la Computación (CACIC 2015), realizado en Sede UNNOBA Junín, del 5 al 9 de octubre de 2015.Red de Universidades con Carreras en Informática (RedUNCI