Related papers: Programming Really Is Simple Mathematics
This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such…
Requirements engineering is crucial to software development but lacks a precise definition of its fundamental concepts. Even the basic definitions in the literature and in industry standards are often vague and verbose. To remedy this…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
We present programming techniques to illustrate the facilities and principles of C++ generic programming using concepts. Concepts are C++'s way to express constraints on generic code. As an initial example, we provide a simple type system…
We give the easily recognizable name "cinnamon" and "cinnamon programming" to a new computation model intended to form a theoretical foundation for Control Network Programming (CNP). CNP has established itself as a programming paradigm…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
This tutorial deal with the Axiom of Choice and some of its applications to topics related to Computer Science. We will see that the Axiom of Choice is equivalent to some well-known proof principles like Zorn's Lemma or Tuckey's Maximality…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
With ever-increasing dataset sizes, subset selection techniques are becoming increasingly important for a plethora of tasks. It is often necessary to guide the subset selection to achieve certain desiderata, which includes focusing or…
Exact real computation is an alternative to floating-point arithmetic where operations on real numbers are performed exactly, without the introduction of rounding errors. When proving the correctness of an implementation, one can focus…
This introduction begins with a section on fundamental notions of mathematical logic, including propositional logic, predicate or first-order logic, completeness, compactness, the L\"owenheim-Skolem theorem, Craig interpolation, Beth's…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…