• DOI:10.4204/EPTCS.351.18
• Corpus ID: 233423167

Canonical automata via distributive law homomorphisms

@inproceedings{Zetzsche2021CanonicalAV,
  title={Canonical automata via distributive law homomorphisms},
  author={Stefan Zetzsche and Gerco van Heerdt and Alexandra Silva and Matteo Sammartino},
  booktitle={MFPS},
  year={2021}
}

• Stefan Zetzsche, Gerco van Heerdt, +1 author Matteo Sammartino
• Published in MFPS 27 April 2021
• Computer Science

The classical powerset construction is a standard method converting a non-deterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that converts an automaton with side-effects, given by a monad, into a deterministic automaton accepting the same language. The resulting automaton has additional algebraic properties, both in the state space and transition structure, inherited from the monad. In this paper, we study the reverse construction and present a framework in which a deterministic automaton with additional algebraic structure over a given monad can be converted into an equivalent succinct automaton with side-effects. Apart from recovering examples from the literature, such as the canonical residual finite-state automaton and the ´atomaton, we discover a new canonical automaton for a regular language by relating the free vector space monad over the two element field to the neighbourhood monad. Finally, we show that every regular language satisfying a suitable property parametric in two monads admits a size-minimal succinct acceptor.