相关论文: Computing Fibonacci numbers on a Turing Machine

Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined.

Two Turing Machines may be able to answer questions about each other that they cannot answer about themselves.

Based on the combinatorial interpretation of the ordered Bell numbers, which count all the ordered partitions of the set $[n]=\{1,2,\dots,n\}$, we introduce the Fibonacci partition as a Fibonacci permutation of its blocks. Then we define…

This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…

We discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the…

We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.

Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.

This essay explores the limits of Turing machines concerning the modeling of minds and suggests alternatives to go beyond those limits.

We consider computations of a Turing machine subjected to noise. In every step, the action (the new state and the new content of the observed cell, the direction of the head movement) can differ from that prescribed by the transition…

The Fibonacci number is the residue of a rational function, from which follows that Fibonacci number summation identities can be derived with the integral representation method, a method also used to derive combinatorial identities. A…

The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…

We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.

In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which…

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and…

The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all)…

An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…

A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather…

We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.

This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…

Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…