Piecewise testable tree languages
Miko{\l}aj Boja\'nczyk (University of Warsaw), Luc Segoufin (INRIA),, Howard Straubing (Boston college)
TL;DR
This paper extends the Simon theorem to tree languages, providing a decidable characterization of those definable by boolean combinations of Sigma_1 sentences, linking language definability to algebraic properties.
Contribution
It introduces a decidable criterion for piecewise testable tree languages, generalizing the Simon theorem from strings to trees.
Findings
Decidable characterization of piecewise testable tree languages
Extension of Simon theorem to tree structures
Connection between language definability and algebraic properties
Abstract
This paper presents a decidable characterization of tree languages that can be defined by a boolean combination of Sigma_1 sentences. This is a tree extension of the Simon theorem, which says that a string language can be defined by a boolean combination of Sigma_1 sentences if and only if its syntactic monoid is J-trivial.
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Taxonomy
TopicsSemantic Web and Ontologies · Natural Language Processing Techniques · Logic, programming, and type systems