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arXiv · 1905.05519

A (co)algebraic theory of succinct automata

Gerco van Heerdt·Joshua Moerman·Matteo Sammartino·Alexandra Silva
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Abstract

The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics---languages over an alphabet---have a common algebraic structure: they are Eilenberg-Moore algebras for the powerset monad. In this paper we study the reverse question to determinization. We will present a construction to associate succinct automata to languages based on different algebraic structures. For instance, for classical regular languages the construction will transform a deterministic automaton into a non-deterministic one, where the states represent the join-irreducibles of the language accepted by a (potentially) larger deterministic automaton. Other examples will yield alternating automata, automata with symmetries, CABA-structured automata, and weighted automata.

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Gerco van Heerdt, Joshua Moerman, Matteo Sammartino, Alexandra Silva. 2019-05-14. A (co)algebraic theory of succinct automata. https://doi.org/10.1016/j.jlamp.2019.02.008

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