We are excited to share that Dr. Anton A. Esin, CEO and Founder of Incarnet Mathematical Modelling, has published a new research article in the prestigious journal AIMS Mathematics (WoS Q1), Volume 10, Issue 4. The article, titled “Finitely Generated Classes of Multi-Argument Logic Functions Excluding Majority and Choice Functions”, marks a significant advance in the structure theory of multi-valued logic.

About the Paper
This paper explores a novel class of logic functions characterised by a structural constraint that excludes two of the most commonly used but computationally complex components: majority and choice functions. Dr. Esin rigorously proves that these classes, although avoiding majority and choice operations, remain finitely generated—opening the door to efficient logical constructions with reduced sensitivity to noise and lower implementation complexity.

Highlights of the Research

• Exclusion of Complex Primitives: The study introduces finitely generated closed classes of multi-argument functions which, unlike traditional models, deliberately omit majority and choice functions—both known for high computational cost and noise sensitivity.
• Finite Generation with Minimal Bases: Esin provides explicit constructions demonstrating that such classes can be generated from compact function sets, even in logics with more than three values.
• Theoretical Impact: The work refines classical results in multi-valued logic by proving structural theorems on closure under superposition and inclusion-exclusion properties with respect to precomplete unary classes.
• Practical Significance: These results bear implications for logic design in telecommunications, quantum computing, and fault-tolerant digital circuits, where computational efficiency and robustness are critical.

Key Implications

• Towards Simpler Circuit Design: The proposed function classes are ideal for use in resource-constrained systems, enabling the design of circuits with fewer logic gates and improved error resistance.
• Relevance to Quantum and AI Systems: By avoiding functions that exhibit sharp transitions or high sensitivity to minor input changes, the paper’s results pave the way for logical models well-suited to quantum channels and machine learning architectures.
• Logical Foundations for Robust Multi-Valued Systems: The theoretical framework aligns closely with the needs of contemporary models in logical inference systems and algebraic logic, offering new directions for the study of closed classes.

Link to the Paper
You can access the full article here:
DOI: 10.3934/math.2025457

About the Author
Dr. Anton A. Esin is a distinguished mathematician specialising in multi-valued logic, computational complexity, and mathematical modelling. His work bridges foundational theory and high-impact applications. Dr. Esin is known for his rigorous contributions to the algebraic structure of logical function classes and their role in advanced digital and quantum systems.

This publication reaffirms the leadership of Incarnet Mathematical Modelling in advancing deep theoretical insights with practical consequences across modern computation and communication technologies. We congratulate Dr. Esin on this important achievement and look forward to future developments.