Related papers: The First Computer Program
Debugging is commonly understood as finding and fixing the cause of a problem. But what does ``cause'' mean? How can we find causes? How can we prove that a cause is a cause--or even ``the'' cause? This paper defines common terms in…
Sophisticated computation methods were developed 4000 years ago in Mesopotamia in the context of scribal schools. The basics of the computation can be detected in clay tablets written by young students educated in these scribal schools. At…
At the intersection of what I call uncomputable art and computational epistemology, a form of experimental philosophy, we find an exciting and promising area of science related to causation with an alternative, possibly best possible,…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of…
This paper presents a brief historical survey of iterative methods for solving linear systems of equations. The journey begins with Gauss who developed the first known method that can be termed iterative. The early 20th century saw good…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
Computer programs do not always work as expected. In fact, ominous warnings about the desperate state of the software industry continue to be released with almost ritualistic regularity. In this paper, we look at the 60 years history of…
Forty years ago, Richard Feynman proposed harnessing quantum physics to build a more powerful kind of computer. Realizing Feynman's vision is one of the grand challenges facing 21st century science and technology. In this article, we'll…
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing…
The main deficiency of the algorithms running on digital computers nowadays is their inability to change themselves during the execution. In line with this, the paper introduces the so-called replicated algorithms, inspired by the concept…
A quantum computer is a hypothetical device in which the laws of quantum mechanics are used to introduce a degree of parallelism into computations and which could therefore significantly improve on the computational speed of a classical…
The Fibonacci numbers are a sequence of integers in which every number after the first two, 0 and 1, is the sum of the two preceding numbers. These numbers are well known and algorithms to compute them are so easy that they are often used…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
In first-year programming courses it is often difficult to show students how an algorithm can be discovered. In this paper we present a program format that supports the development from specification to code in small and obvious steps; that…
Licklider advocated in 1960 the construction of computers capable of working symbiotically with humans to address problems not easily addressed by humans working alone. Since that time, many of the advances that he envisioned have been…
A quantum computer has now solved a specialized problem believed to be intractable for supercomputers, suggesting that quantum processors may soon outperform supercomputers on scientifically important problems. But flaws in each quantum…
The history of the development of Monte Carlo methods to solve the many-body problem in quantum mechanics is presented. The survey starts with the early attempts with the first available computers just after the war and extends until the…