Lifting Adjunctions to Coalgebras to (Re)Discover Automata Constructions

Conference paper

DOI: 10.1007/978-3-662-44124-4_10

Volume 8446 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Kerstan H., König B., Westerbaan B. (2014) Lifting Adjunctions to Coalgebras to (Re)Discover Automata Constructions. In: Bonsangue M. (eds) Coalgebraic Methods in Computer Science. CMCS 2014. Lecture Notes in Computer Science, vol 8446. Springer, Berlin, Heidelberg

Abstract

It is a well-known fact that a nondeterministic automaton can be transformed into an equivalent deterministic automaton via the powerset construction. From a categorical perspective this construction is the right adjoint to the inclusion functor from the category of deterministic automata to the category of nondeterministic automata. This is in fact an adjunction between two categories of coalgebras: deterministic automata are coalgebras over \(\mathbf {Set}\) and nondeterministic automata are coalgebras over \(\mathbf {Rel}\). We will argue that this adjunction between coalgebras originates from a canonical adjunction between \(\mathbf {Set}\) and \(\mathbf {Rel}\).

In this paper we describe how, in a quite generic setting, an adjunction can be lifted to coalgebras, and we compare some sufficient conditions. Then we illustrate this technique in length: we recover several constructions on automata as liftings of basic adjunctions including determinization of nondeterministic and join automata, codeterminization, and the dualization of linear weighted automata. Finally, we show how to use the lifted adjunction to check behavioral equivalence.

Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Henning Kerstan
    • 1
  • Barbara König
    • 1
  • Bram Westerbaan
    • 2
  1. 1.Universität Duisburg-EssenEssenGermany
  2. 2.Radboud Universiteit NijmegenNijmegenThe Netherlands