Year: 2025
Type: preprint
Abstract: We show a theorem on monadic second-order k-ary queries on finite words. It may be illustrated by the following example: if the number of results of a query on binary strings is O(number of 0s $\times$ number of 1s), then each result can be MSO-definably identified from a 0-position, a 1-position and some finite data. Our proofs also handle the case of first-order logic / aperiodic monoids. Thus we can state and prove the folklore theorem that dimension minimisation holds for first-order string-to-string interpretations.
Source: arXiv (Cornell University)
Authors: Nguyên, Lê Thành Dũng, Parys, Paweł
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7110995270
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