# A (co)algebraic theory of succinct automata

1 Jun 2019

Gerco van Heerdt, Joshua Moerman, Matteo Sammartino, and Alexandra Silva

## 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 semanticsâ€”languages over an alphabetâ€”have a common algebraic structure: they are Eilenberg-Moore algebras for the powersetgen 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.