On the decomposition of stochastic cellular automata

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the evolution of the stochastic cellular automaton. The second property shows that stochastic cellular automata are equivalent to so-called stochastic mixtures of deterministic cellular automata. Based on this property, any stochastic cellular automaton can be decomposed into a set of deterministic cellular automata, each of which contributes to the behavior of the stochastic cellular automaton.Comment: Submitted to Journal of Computation Science, Special Issue on Cellular Automata Application

Cellular Automata Applications in Shortest Path Problem

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineering problems. Among them, the shortest path problem is one of the most pronounced and highly studied problems that scientists have been trying to tackle by using a plethora of methodologies and even unconventional approaches. The proposed solutions are mainly justified by their ability to provide a correct solution in a better time complexity than the renowned Dijkstra's algorithm. Although there is a wide variety regarding the algorithmic complexity of the algorithms suggested, spanning from simplistic graph traversal algorithms to complex nature inspired and bio-mimicking algorithms, in this chapter we focus on the successful application of CAs to shortest path problem as found in various diverse disciplines like computer science, swarm robotics, computer networks, decision science and biomimicking of biological organisms' behaviour. In particular, an introduction on the first CA-based algorithm tackling the shortest path problem is provided in detail. After the short presentation of shortest path algorithms arriving from the relaxization of the CAs principles, the application of the CA-based shortest path definition on the coordinated motion of swarm robotics is also introduced. Moreover, the CA based application of shortest path finding in computer networks is presented in brief. Finally, a CA that models exactly the behavior of a biological organism, namely the Physarum's behavior, finding the minimum-length path between two points in a labyrinth is given.Comment: To appear in the book: Adamatzky, A (Ed.) Shortest path solvers. From software to wetware. Springer, 201

Bipolar fuzzy sets in switchboard automata and optimisation problems

Bipolar fuzzy sets can be extended to triangular bipolar fuzzy number and are applied in optimisation problems, specifically critical path problem and reliability system of an automobile. Some of the properties of triangular bipolar fuzzy numbers are introduced and used in critical path problems to find a bipolar fuzzy critical path. As a result, acceptance area and rejection area could be recognised successfully. By using a tree diagram, triangular bipolar fuzzy number is then applied to a reliability system of an automobile in order to find the failure rate to start of an automobile that is based on the ideas of circuits which are connected to the system. An illustrative example is presented and the tolerance level of acceptence (positive membership value) and tolerance level of rejection (negative membership value) could be determined successfully in a reliability system of an automobile. In automata theory, the decomposition theorem for bipolar fuzzy finite state automata and its transformations semigroups are initiated and discussed in order to enrich the structure of algebraic properties in bipolar fuzzy finite state automata. Furthermore, the idea of bipolar general fuzzy finite switchboard automata and asynchronous bipolar general fuzzy switchboard automata is initiated. In particular, the algebraic properties of bipolar general fuzzy switchboard automata are discussed in term of switching and commutative by proving the theorems that are related into these concepts. Finally, the notion of the switchboard subsystems and strong switchboard subsystem of bipolar general fuzzy switchboard automata are initiated. As a result, it can be concluded that every switchboard subsystem is a strong switchboard subsystem throughout the proven theorems. As an application, a concept of Lowen fuzzy topology is induced in switchboard subsystem of bipolar general fuzzy switchboard automata by using Kuratowski closure operator

A Formal Approach based on Fuzzy Logic for the Specification of Component-Based Interactive Systems

Formal methods are widely recognized as a powerful engineering method for the specification, simulation, development, and verification of distributed interactive systems. However, most formal methods rely on a two-valued logic, and are therefore limited to the axioms of that logic: a specification is valid or invalid, component behavior is realizable or not, safety properties hold or are violated, systems are available or unavailable. Especially when the problem domain entails uncertainty, impreciseness, and vagueness, the appliance of such methods becomes a challenging task. In order to overcome the limitations resulting from the strict modus operandi of formal methods, the main objective of this work is to relax the boolean notion of formal specifications by using fuzzy logic. The present approach is based on Focus theory, a model-based and strictly formal method for componentbased interactive systems. The contribution of this work is twofold: i) we introduce a specification technique based on fuzzy logic which can be used on top of Focus to develop formal specifications in a qualitative fashion; ii) we partially extend Focus theory to a fuzzy one which allows the specification of fuzzy components and fuzzy interactions. While the former provides a methodology for approximating I/O behaviors under imprecision, the latter enables to capture a more quantitative view of specification properties such as realizability.Comment: In Proceedings FESCA 2015, arXiv:1503.0437

Weighted lattice polynomials

We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We also show that these functions include the class of discrete Sugeno integrals and that they are characterized by a median based decomposition formula.Comment: Revised version (minor changes