arXiv subjects

Adam Mata

Publications and source records attributed to Adam Mata.

2 recordsLinked to original sources

arXiv2025

Infinite convex geometries with lower semi-modularity and join semi-distributivity

The following article treats about convex geometries which are lower semi-modular and join semi-distributive lattices. Firstly, it is shown that there is a class $K$ of infinite convex geometries which can be build out of finite ones by using the construction of a union of a chain. Then it is shown that elements of $K$ preserve lower semi-modularity and join semi-distributivity which are not default properties in the infinite setting. It is also discussed that not all of the infinite convex geometries may be obtained by the means of the union of a chain.

math.LO↗

arXiv2024

Probabilistic Shoenfield Machines

The article provides the theoretical framework of Probabilistic Shoenfield Machines (PSMs), an extension of the classical Shoenfield Machine that models randomness in the computation process. PSMs are introduced in contexts where deterministic computation is insufficient, such as randomized algorithms. By allowing transitions to multiple possible states with certain probabilities, PSMs can solve problems and make decisions based on probabilistic outcomes, thus expanding the variety of possible computations. We provide an overview of PSMs, detailing their formal definitions, the computation mechanism, and their equivalence with Non-deterministic Shoenfield Machines (NSMs)

cs.SC↗