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Tameness and the power of programs over monoids in DA

Abstract : The program-over-monoid model of computation originates with Barrington's proof that it captures the complexity class 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 DA satisfies tameness and hence that the regular languages recognized by programs over monoids in DA are precisely those recognizable in the classical sense by morphisms from QDA. Third, we show by contrast that the well studied class of monoids called J is not tame. Finally, we exhibit a program-length-based hierarchy within the class of languages recognized by programs over monoids from DA.
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https://hal.archives-ouvertes.fr/hal-03114304
Contributor : Nathan Grosshans <>
Submitted on : Monday, January 18, 2021 - 6:50:49 PM
Last modification on : Tuesday, May 4, 2021 - 2:06:03 PM
Long-term archiving on: : Monday, April 19, 2021 - 7:52:03 PM

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  • HAL Id : hal-03114304, version 1
  • ARXIV : 2101.07495

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Nathan Grosshans, Pierre Mckenzie, Luc Segoufin. Tameness and the power of programs over monoids in DA. 2021. ⟨hal-03114304⟩

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