A criterion for the simplicity of finite Moore automata

A Moore automaton A = (A, X,Y,S, A) can be obtained in two steps: first we consider the triplet (A, X, 6) - called a semiautomaton and denoted by S — and then we add the components Y and A which concern the output functioning. Our approach is: S is supposed to be fixed, we vary A in any possible way, and - among the resulting automata - we want to separate the simple and the nonsimple ones from each other. This task is treated by combinatorial methods. Concerning the efficiency of the procedure, we note that it uses a semiautomaton having |A|(|A| + l)/2 states

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks

In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of \tit{cellular networks} and \tit{random graphs}. One of our main themes is the development of the concept of \tit{physical (proto)points} or \tit{lumps} as densely entangled subcomplexes of the network and their respective web, establishing something like \tit{(proto)causality}. It may perhaps be said that certain parts of our programme are realisations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this \tit{two-story-concept} of \tit{quantum} space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality.Comment: 35 pages, Latex, under consideration by CQ