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Answer set programming (ASP) is a logic programming formalism used in various areas of artificial intelligence like combinatorial problem solving and knowledge representation and reasoning. It is known that enhancing ASP with function…

BSS RAMs over first-order structures help to characterize algorithms for processing objects by means of useful operations and relations. They are the result of a generalization of several types of abstract machines. We want to discuss…

We study in-network computation on general network topologies. Specifically, we are given the description of a function, and a network with distinct nodes at which the operands of the function are made available, and a designated sink where…

Concerning classical computational models able to express all the Primitive Recursive Functions (PRF), there are interesting results regarding limits on their algorithmic expressiveness or, equivalently, efficiency, namely the ability to…

This paper studies the minimal length representation of the natural numbers. Let O be a fixed set of integer-valued functions (primarily hyperoperations). For each n, what is the shortest way of expressing n as a combinations of functions…

Partial functions are common abstractions in formal specification notations such as Z, B and Alloy. Conversely, executable programming languages usually provide little or no support for them. In this paper we propose to add partial…

Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…

The paper exploits an isomorphism between the natural numbers N and a space U of periodic sequences of the roots of unity in constructing a recursive procedure for representing and computing the prime numbers. The nth wave number ${\bf…

Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…

We present a notion of primitive which corresponds exactly with the Riemann integral. We obtain a characterization of the integrability in the sense of Riemann which produces a Fundamental Theorem of Calculus without special assumptions. We…

Consideration of a classification of the number of partitions of a natural number according to the members of sub-partitions differing from unity leads to a non-recursive formula for the number of irreducible representations of the…

The famous asynchronous computability theorem (ACT) relates the existence of an asynchronous wait-free shared memory protocol for solving a task with the existence of a simplicial map from a subdivision of the simplicial complex…

The notion of $b$-regular sequences was generalized to abstract numeration systems by Maes and Rigo in 2002. Their definition is based on a notion of $\mathcal{S}$-kernel that extends that of $b$-kernel. However, this definition does not…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

Replication studies estimate the replicability rate of scientific results by aggregating binary verdicts of experiments. Exact replications are rarely attainable, so most replication sequences are non-exact. Experiments differ in ways that…

We study nominal recursors from the literature on syntax with bindings and compare them with respect to expressiveness. The term "nominal" refers to the fact that these recursors operate on a syntax representation where the names of bound…

Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…

Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…

In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of…

Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…