Related papers: On the formalization of the notion of a concurrent…
An earlier paper gives an account of a quest for a satisfactory formalization of the classical informal notion of an algorithm. That notion only covers algorithms that are deterministic and non-interactive. In this paper, an attempt is made…
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 ubiquity of networking infrastructure in modern life necessitates scrutiny into networking fundamentals to ensure the safety and security of that infrastructure. The formalization of concurrent algorithms, a cornerstone of networking,…
Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
This article aims to describe and explain the theoretical foundations of concurrent and set concurrent algorithms, considering an asynchronous shared memory system where any number of processes can crash. Verification of concurrent…
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…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
Common approaches to concurrent programming begin with languages whose semantics are naturally sequential and add new constructs that provide limited access to concurrency, as exemplified by futures. This approach has been quite successful,…
We introduce parallelism into the basic algebra of games to model concurrent game algebraically. Parallelism is treated as a new kind of game operation. The resulted algebra of concurrent games can be used widely to reason the parallel…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Game-theoretical approach to the analysis of parallel algorithms is proposed. The approach is based on presentation of the parallel computing as a congestion game. In the game processes compete for resources such as core of a central…
Efforts to promote equitable public policy with algorithms appear to be fundamentally constrained by the "impossibility of fairness" (an incompatibility between mathematical definitions of fairness). This technical limitation raises a…
This paper proposes a way to effectively compare the potential of processes to cause conflict. In discrete event systems theory, two concurrent systems are said to be in conflict if they can get trapped in a situation where they are both…
This dialog paper offers a preview and provides a foretaste of an upcoming work on the axiomatization of basic interactive algorithms. The modern notion of algorithm was elucidated in the 1930s--1950s. It was axiomatized a quarter of a…
With the increasing capabilities of Large Language Models (LLMs), parallel reasoning has emerged as a new inference paradigm that enhances reasoning robustness by concurrently exploring multiple lines of thought before converging on a final…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
Machine learning algorithms for prediction are increasingly being used in critical decisions affecting human lives. Various fairness formalizations, with no firm consensus yet, are employed to prevent such algorithms from systematically…