Related papers: Complexity of Linear Subsequences of Fibonacci-Aut…
Following a recent paper of Anselmo et al., we consider $m \times n$ rectangular matrices formed from the Fibonacci word, and we show that their balance properties can be solved with a finite automaton. We also generalize the result to…
A natural generalization of base B expansions is Zeckendorf's Theorem: every integer can be uniquely written as a sum of non-consecutive Fibonacci numbers $\{F_n\}$, with $F_{n+1} = F_n + F_{n-1}$ and $F_1=1, F_2=2$. If instead we allow the…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
We study a robot snake model based on a discrete linear control system involving Fibonacci sequence and closely related to the theory of expansions in non-integer bases. The present paper includes an investigation of the reachable…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-10 expansions, Dedekind cuts and continued fractions.
Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…
Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbour interaction and two kinds of atoms (mass-ratio $r$) arranged according to the self-similar binary Fibonacci sequence $ABAABABA...$, which is obtained by…
We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton.…
We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the language of automata theory and adapt a recent algorithm for…
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n. We analyze…
Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Buechi acceptance condition---a basic notion in the theory of automata for infinite words or trees.…
Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial…
Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…
Certain famous combinatorial sequences, such as the Catalan numbers and the Motzkin numbers, when taken modulo a prime power, can be computed by finite automata. Many theorems about such sequences can therefore be proved using Walnut, which…
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of…
Finite-state transducers give efficient representations of many Natural Language phenomena. They allow to account for complex lexicon restrictions encountered, without involving the use of a large set of complex rules difficult to analyze.…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Symbolic Finite Automata and Register Automata are two orthogonal extensions of finite automata motivated by real-world problems where data may have unbounded domains. These automata address a demand for a model over large or infinite…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…