TL;DR
This paper extends algebraic theory to forest algebras, providing new proofs for characterizations of tree languages, thereby advancing the mathematical understanding of tree language classification.
Contribution
It introduces an extension of Tilson's algebraic theory to forest algebras and offers a new proof of a key characterization of locally testable tree languages.
Findings
Extended Tilson's theory to forest algebras
Provided a new proof for characterizing locally testable tree languages
Demonstrated the usefulness of algebraic methods in tree language theory
Abstract
We extend Tilson's theory of the algebra of finite categories, in particular, the Derived Category Theorem, to the setting of forest algebras. As an illustration of the usefulness of this method, we provide a new proof of a result of Place and Segoufin characterizing locally testable tree languages.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Algebraic structures and combinatorial models