Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m ≥ 2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of mN in the Fibonacci system is exactly 2m.

Power law fluctuations and scale-free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova-type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study, and is capable of generating critical exponents matching experiments. Our main obs...

An efficient data structure for representing the full index of a set of strings is the factor automaton, the minimal deterministic automaton representing the set of all factors or substrings of these strings. This paper presents a novel analysis of the size of the factor automaton of an automaton, that is the minimal deterministic automaton accepting the set of factors of a finite set of string...

We have implemented a package that transforms concise algebraic descriptions of linear block codes into finite automata representations, and also generates decoders from such representations. The transformation takes a description of the code in the form of a k × n generator matrix over a field with q elements, representing a finite language containing q strings, and constructs a minimal automa...

in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...

The minimization of nondeterministic automata without initial states (developed within a game-theoretic framework in Calude, Calude, Khoussainov [3]) is presented in terms of bisimulations; the minimal automaton is unique up to an isomorphism in case of reversible automata. We also prove that there exists an infinite class of (strongly connected) nondeterministic automata each of which is not b...

A group automaton is a complete deterministic automaton such that each letter of the alphabet acts on the set of states as a permutation 1, 5]. The aim is to describe an algorithm for the random generation of a minimal group automaton with n states. The treatment is largely based on properties of random permutations and random automata.

We propose a representation of simple conceptual graphs with binary conceptual relations, which is based on finite-state automata. The representation enables the calculation of injective projection as a two-stage process: off-line calculation of the computationally-intensive subsumption checks and encoding of the results as a minimal finite-state automaton, and run-time calculation by look-up i...

We describe a tool that inputs a deterministic ω-automaton with any acceptance condition, and synthesizes an equivalent ω-automaton with another arbitrary acceptance condition and a given number of states, if such an automaton exists. This tool, that relies on a SAT-based encoding of the problem, can be used to provide minimal ω-automata equivalent to given properties, for different acceptance ...