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Matrix Representation of Virus Machines and an Application to the Discrete Logarithm Problem
Antonio Ramírez-de-Arellano1,2, David Orellana-Martín2,3, Mario J Pérez-Jiménez2,3
1Research Institute for Artificial Intelligence Mihai Drăgănescu, Calea 13 Septembrie 050711, Bucharest, Romania.
International Journal of Neural Systems
|August 19, 2025
Summary
This study introduces a matrix-based representation for virus machines, enhancing their computational analysis. This new method clarifies complex computations and invariants, aiding in understanding these powerful algorithms.
Area of Science:
- * Computational theory and artificial intelligence.
- * Mathematical modeling of biological systems.
Background:
- * Virus machines offer novel computational models inspired by viral spread.
- * They possess significant computational power for complex problems.
- * Traditional representations can be limiting for analysis.
Purpose of the Study:
- * To introduce an extended matrix-based representation for virus machines.
- * To describe virus machine computations using linear algebra.
- * To demonstrate invariants for proof purposes.
Main Methods:
- * Representing hosts, virus counts, and transmission rules as vectors and matrices.
- * Utilizing linear algebra operations to define virus machine computations.
- * Applying the matrix representation to identify machine invariants.
Main Results:
- * A novel matrix-based framework for virus machines is presented.
- * Computations and invariants are described using linear algebra.
- * The representation is validated with a virus machine example.
Conclusions:
- * The matrix representation provides a clear framework for analyzing virus machines.
- * This approach facilitates the study of invariants and computational properties.
- * It offers a powerful tool for understanding complex computational models.
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