Related papers: Complexity of Linear Subsequences of Fibonacci-Aut…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
We study the complexity of basic regular operations on languages represented by incomplete deterministic or nondeterministic automata, in which all states are final. Such languages are known to be prefix-closed. We get tight bounds on both…
We consider finite two-way automata and measure the use of two-way motion by counting the number of left moves in accepting computations. Restriction of the automata according to this measure allows us to study in detail the use of two-way…
We consist of first presenting Zeckendorf Theorem with these two versions Fibonacci and Luca. In this document we obtain results on the generalized of the Zeckendorf theorem for Fibonacci numbers (multibonacci). Such results find…
We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the…
We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…
One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer…
Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
We introduce classical and non-deterministic finite automata associated with representations of the braid group. After briefly reviewing basic definitions on finite automata, Coxeter's groups and the associated word problem, we turn to the…
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata…
Following up on a paper of Balamohan, Kuznetsov, and Tanny, we analyze a variant of Hofstadter's Q-sequence and show it is 2-automatic. An automaton computing the sequence is explicitly given.
In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first…
In this paper, we consider the transition complexity of regular languages based on the incomplete deterministic finite automata. A number of results on Boolean operations have been obtained. It is shown that the transition complexity…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence related more general classes of regular…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
The focus of this note is to formulate the algorithms and give the examples used by Fibonacci in Liber Abaci to expand any fraction into a sum of unit fractions. The description in Liber Abaci is all verbal and the examples are numbers…