Related papers: Computing Fibonacci numbers on a Turing Machine
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
This note contains a report of a proof by computer that the Fibonacci group F(2,9) is automatic. The automatic structure can be used to solve the word problem in the group. Furthermore, it can be seen directly from the word-acceptor that…
We give several different encodings of the step function of a Turing machine in intuitionistic linear logic, and calculate the denotations of these encodings in the Sweedler semantics.
A consistently specified halting function may be computed.
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
Is there any hope for quantum computing to challenge the Turing barrier, i.e. to solve an undecidable problem, to compute an uncomputable function? According to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens the…
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic…
Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing…
Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows…
In this paper, we find all the sums of three Fibonacci numbers which are close to a power of 2. This paper continues and extends the previous work of Hasanalizade \cite{Hasanalizade}.
We consider computations of a Turing machine under noise that causes consecutive violations of the machine's transition function. Given a constant upper bound B on the size of bursts of faults, we construct a Turing machine M(B) subject to…
It is shown that the unique representation of positive integers in terms of tribonacci numbers and the unique representation in terms of iterated A, B and C sequences defined from the tribonacci word are equivalent. Two auxiliary…
Tur\'an number is one of primary topics in the combinatorics of finite sets,in this paper, we will present a new upper bound for Tur\'an number.
In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and investigate their properties.
This paper investigates a variety of unconventional quantum computation devices, including fermionic quantum computers and computers that exploit nonlinear quantum mechanics. It is shown that unconventional quantum computing devices can in…
We prove that the maximum speed and the entropy of a one-tape Turing machine are computable, in the sense that we can approximate them to any given precision $\epsilon$. This is contrary to popular belief, as all dynamical properties are…
Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…
We give enumerations of various families of restricted permutations involving the Fibonacci numbers or k-generalized Fibonacci numbers.
A quantum algorithm for the calculation of $\pi$ is proposed and implemented on the five-qubit IBM quantum computer with superconducting qubits. We find $\pi=3.157\pm0.017$. The error is due to the noise of quantum one-qubit operations and…
I give a brief overview of fault-tolerant quantum computation, with an emphasis on recent work and open questions.