A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

Near-Optimal Scheduling for LTL with Future Discounting

We study the search problem for optimal schedulers for the linear temporal logic (LTL) with future discounting. The logic, introduced by Almagor, Boker and Kupferman, is a quantitative variant of LTL in which an event in the far future has only discounted contribution to a truth value (that is a real number in the unit interval [0, 1]). The precise problem we study---it naturally arises e.g. in search for a scheduler that recovers from an internal error state as soon as possible---is the following: given a Kripke frame, a formula and a number in [0, 1] called a margin, find a path of the Kripke frame that is optimal with respect to the formula up to the prescribed margin (a truly optimal path may not exist). We present an algorithm for the problem; it works even in the extended setting with propositional quality operators, a setting where (threshold) model-checking is known to be undecidable

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

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

(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces

We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may it also view as a dynamical randomisation of the causal-set framework developed by e.g. Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor changes added relating to previous wor

Controlled Fuzzy Parallel Rewriting

We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show (i) regular control does not provide additional generating power to the model, (ii) the number of fuzzy substitutions in the underlying iteration grammar can be reduced to two, and (iii) the resulting family of fuzzy languages possesses strong closure properties, viz. it is a full hyper-AFFL, i.e., a hyper-algebraically closed full Abstract Family of Fuzzy Languages