相关论文: Towards a Definition of an Algorithm

People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue…

This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs,…

Although algorithm is one of the central subjects, there have been little common understandings of what an algorithm is. For example, Gurevich view algorithms as abstract state machines, while others view algorithms as recursors. We promote…

The starting point of this paper is a collection of properties of an algorithm that have been distilled from the informal descriptions of what an algorithm is that are given in standard works from the mathematical and computer science…

The question of the definition of what is an algorithm is recurrent. It is found in teaching, at different levels and particularly in secondary education because of the recent evolutions in high school, with immediate consequences in higher…

In this paper we give a definition of "algorithm," "finite algorithm," "equivalent algorithms," and what it means for a single algorithm to dominate a set of algorithms. We define a derived algorithm which may have a smaller mean execution…

A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…

This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…

This paper proposes a new view to algorithms, Algorithms as defining dynamic systems. This view extends the traditional, deterministic view that an algorithm is a step by step procedure with nondeterminism. As a dynamic system can be…

A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…

According to some algorithmicists, algorithmics traditionally uses algorithm theory, which stems from mathematics. The growing need for innovative algorithms has caused increasing gaps between theory and practice. Originally, this motivated…

This paper proposes a new approach to defining and expressing algorithms: the notion of {\it task logical} algorithms. This notion allows the user to define an algorithm for a task $T$ as a set of agents who can collectively perform $T$.…

While the engineering of operating systems is well understood, their formal structure and properties are not. The latter needs a clear definition of the purpose of an OS and an identification of the core. In this paper I offer definitions…

Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A…

Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non homogeneous algorithms. Although both classes contain algorithms with…

We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…

Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…

When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor twist on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…

When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor variation on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…

The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…