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Journal Articles Logical Methods in Computer Science Year : 2022

Tameness and the power of programs over monoids in DA

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Nathan Grosshans
Luc Segoufin
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Abstract

The program-over-monoid model of computation originates with Barrington's proof that the model captures the complexity class $\mathsf{NC^1}$. Here we make progress in understanding the subtleties of the model. First, we identify a new tameness condition on a class of monoids that entails a natural characterization of the regular languages recognizable by programs over monoids from the class. Second, we prove that the class known as $\mathbf{DA}$ satisfies tameness and hence that the regular languages recognized by programs over monoids in $\mathbf{DA}$ are precisely those recognizable in the classical sense by morphisms from $\mathbf{QDA}$. Third, we show by contrast that the well studied class of monoids called $\mathbf{J}$ is not tame. Finally, we exhibit a program-length-based hierarchy within the class of languages recognized by programs over monoids from $\mathbf{DA}$.
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Dates and versions

hal-03114304 , version 1 (18-01-2021)
hal-03114304 , version 2 (03-01-2022)
hal-03114304 , version 3 (05-05-2022)

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Nathan Grosshans, Pierre Mckenzie, Luc Segoufin. Tameness and the power of programs over monoids in DA. Logical Methods in Computer Science, 2022, 18 (3), pp.14:1-14:34. ⟨10.46298/lmcs-18(3:14)2022⟩. ⟨hal-03114304v3⟩
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