Fibrations of Tree Automata

Colin Riba (1, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages

We propose a notion of morphisms between tree automata based on game semantics. Morphisms are winning strategies on a synchronous restriction of the linear implication between acceptance games. This leads to split indexed categories, with substitution based on a suitable notion of synchronous tree function. By restricting to tree functions issued from maps on alphabets, this gives a fibration of tree automata. We then discuss the (fibrewise) monoidal structure issued from the synchronous product of automata. We also discuss how a variant of the usual projection operation on automata leads to an existential quantification in the fibered sense. Our notion of morphism is correctin the sense that it respects language inclusion, and in a weaker sense also complete.

Keywords: Tree automata; Game semantics; Categorical Logic

Domains: Logic in Computer Science [cs.LO]

Colin Riba. Fibrations of Tree Automata. TLCA 2015, Jul 2015, Varsovie, Poland. pp.302--316, ⟨10.4230/LIPIcs.TLCA.2015.302⟩. ⟨hal-01261182⟩