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To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…
The field of quantum computing is at an exciting time where we are constructing novel hardware, evaluating algorithms, and finding out what works best. As qubit technology grows and matures, we need to be ready to design and program larger…
One of the roots of evolutionary computation was the idea of Turing about unorganized machines. The goal of this work is the development of foundations for evolutionary computations, connecting Turing's ideas and the contemporary state of…
Reading comprehension models have been successfully applied to extractive text answers, but it is unclear how best to generalize these models to abstractive numerical answers. We enable a BERT-based reading comprehension model to perform…
A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach…
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental…
A re-construction of the fundamentals of programming as a small mathematical theory (PRISM) based on elementary set theory. Highlights: $\bullet$ Zero axioms. No properties are assumed, all are proved (from standard set theory). $\bullet$ A…
Existing abstract models of quantum computation make reference to circuit elements, much in contrast to their classical counterparts. Circuits, as a model of computation, substantially limit algorithmic expression and obscure high-level…
Abduction is one of the most important forms of reasoning; it has been successfully applied to several practical problems such as diagnosis. In this paper we investigate whether the computational complexity of abduction can be reduced by an…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
How well one can copy an arbitrary qubit? To answer this question we consider two arbitrary vectors in a two-dimensional state space and an abstract copying transformation which will copy these two vectors. If the vectors are orthogonal,…
Object-oriented programming (OOP) is aimed at describing the structure and behaviour of objects by hiding the mechanism of their representation and access in primitive references. In this article we describe an approach, called…
This paper examines conceptual models and their application to computational thinking. Computational thinking is a fundamental skill for everybody, not just for computer scientists. It has been promoted as skills that are as fundamental for…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.
In order to achieve competitive performance, abstract machines for Prolog and related languages end up being large and intricate, and incorporate sophisticated optimizations, both at the design and at the implementation levels. At the same…
The invention of CPU-centric computing paradigm was incredible breakthrough of computer science that revolutionized our everyday life dramatically. However, the CPU- centric paradigm is based on the Turing machine concept and, as a result,…
Quantum computation is a rapidly progressing field today. What are its principles? In what sense is it distinct from conventional computation? What are its advantages and disadvantages? What type of problems can it address? How practical is…
The asynchronous computability theorem (ACT) uses concepts from combinatorial topology to characterize which tasks have wait-free solutions in read-write memory. A task can be expressed as a relation between two chromatic simplicial…