A (co)algebraic theory of succinct automata
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.
Keywords
Cite
@article{arxiv.1905.05519,
title = {A (co)algebraic theory of succinct automata},
author = {Gerco van Heerdt and Joshua Moerman and Matteo Sammartino and Alexandra Silva},
journal= {arXiv preprint arXiv:1905.05519},
year = {2019}
}