Related papers: Abstract Computability, Algebraic Specification an…
Comparison to traditionally accurate computing, approximate computing focuses on the rapidity of the satisfactory solution, but not the unnecessary accuracy of the solution. Approximate bisimularity is the approximate one corresponding to…
In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine…
In our previous work, we have constructed explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds. This paper presents its variant. Our result is new in obtaining…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…
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…
We present axiomatisations for a number of partial function signatures that include domain restriction, modelled as a right normal band operation. Other operations considered are override and update, difference, minus, intersection,…
Computer algorithms are written with the intent that when run they perform a useful function. Typically any information obtained is unknown until the algorithm is run. However, if the behavior of an algorithm can be fully described by…
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
We give a number of formal proofs of theorems from the field of computable analysis. Many of our results specify executable algorithms that work on infinite inputs by means of operating on finite approximations and are proven correct in the…
The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
In various applications, computers are required to compute approximations to univariate elementary and special functions such as $\exp$ and $\arctan$ to modest accuracy. This paper proposes a new heuristic for automating the design of such…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…