Elsevier

Theoretical Computer Science

Volume 604, 2 November 2015, Pages 81-101
Theoretical Computer Science

Coalgebraic constructions of canonical nondeterministic automata

https://doi.org/10.1016/j.tcs.2015.03.035Get rights and content
Under an Elsevier user license
open archive

Abstract

For each regular language L we describe a family of canonical nondeterministic acceptors (nfas). Their construction follows a uniform recipe: build the minimal dfa for L in a locally finite variety V, and apply an equivalence between the category of finite V-algebras and a suitable category of finite structured sets and relations. By instantiating this to different varieties, we recover three well-studied canonical nfas: V = boolean algebras yields the átomaton of Brzozowski and Tamm, V = semilattices yields the jiromaton of Denis, Lemay and Terlutte, and V=Z2-vector spaces yields the minimal xor automaton of Vuillemin and Gama. Moreover, we obtain a new canonical nfa called the distromaton by taking V = distributive lattices. Each of these nfas is shown to be minimal relative to a suitable measure, and we derive sufficient conditions for their state-minimality. Our approach is coalgebraic, exhibiting additional structure and universal properties of the canonical nfas.

Keywords

Non-deterministic automata
Join-semilattices
Coalgebras
Minimization

Cited by (0)

1

Stefan Milius acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) under project MI 717/5-1.