Combinatorial results to measure the complexity of quantifier free formulas in algebraic systems

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Author list: Kumduang, T.; Sriwongsa, S.; Wattanatripop, K.

Publisher: World Scientific Publishing

Publication year: 2025

Journal: Asian-European Journal of Mathematics (1793-5571)

Start page: 2550126

ISSN: 1793-5571

eISSN: 1793-7183

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-105020822761&doi=10.1142%2FS1793557125501268&partnerID=40&md5=10707c8065b202f100bc40d3213ee730

Languages: English-Great Britain (EN-GB)

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Abstract

The complexity of terms of type τ of an algebra of type τ can be measured by several methods, including the depth of a term, the total number of variables or operation symbols that appear in a term and the length of a term. Generally, algebraic systems can be viewed as a generalization of algebras. To describe properties of algebraic systems of arbitrary types, quantifier free formulas of type (τ,τ′) induced by terms, relation symbols, and logical connectors are essential. In this paper, we aim to define various measurements of the complexity of quantifier free formulas and then formalize these measurements under different operations. Applications of these explicit formulas for some classes of mappings are provided. © 2025 World Scientific Publishing Company.

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