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The Power of Programs over Monoids in J

Nathan Grosshans 1, 2
1 VALDA - Value from Data
DI-ENS - Département d'informatique de l'École normale supérieure, Inria de Paris
Abstract : The model of programs over (finite) monoids, introduced by Barrington and Thérien, gives an interesting way to characterise the circuit complexity class $\mathsf{NC^1}$ and its subclasses and showcases deep connections with algebraic automata theory. In this article, we investigate the computational power of programs over monoids in $\mathbf{J}$, a small variety of finite aperiodic monoids. First, we give a fine hierarchy within the class of languages recognised by programs over monoids from $\mathbf{J}$, based on the length of programs but also some parametrisation of $\mathbf{J}$. Second, and most importantly, we make progress in understanding what regular languages can be recognised by programs over monoids in $\mathbf{J}$. We show that those programs actually can recognise all languages from a class of restricted dot-depth one languages, using a non-trivial trick, and conjecture that this class suffices to characterise the regular languages recognised by programs over monoids in $\mathbf{J}$.
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Submitted on : Tuesday, December 17, 2019 - 12:34:22 PM
Last modification on : Tuesday, May 4, 2021 - 2:06:03 PM
Long-term archiving on: : Wednesday, March 18, 2020 - 1:08:11 PM

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Nathan Grosshans. The Power of Programs over Monoids in J. LATA 2020 - 14th International Conference on Language and Automata Theory and Applications, Mar 2020, Milan, Italy. ⟨10.1007/978-3-030-40608-0_22⟩. ⟨hal-02414771⟩

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