A syntactic congruence for languages of birooted trees

Achim Blumensath 1 David Janin 2, 3
3 PoSET - Models for a Structured Programming of Space and Time
LaBRI - Laboratoire Bordelais de Recherche en Informatique, SCRIME - Studio de Création et de Recherche en Informatique et Musique Électroacoustique, Inria Bordeaux - Sud-Ouest
Abstract : The study of languages of labelled birooted trees, that is, elements of the free inverse monoid enriched by a vertex labelling, has led to the notion of quasi-recognisability. It generalises the usual notion of recognisability by replacing homomorphisms by certain prehomomorphism into finite ordered monoids, called adequate, that only preserve some products: the so-called disjoint ones. In this paper we study the underlying partial algebra setting and we define a suitable notion of a syntactic congruence such that (i) having a syntactic congruence of finite index captures MSO-definability; (ii) a certain order-bisimulation refinement of the syntactic congruence captures quasi-recognisability in the same way.
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Submitted on : Monday, February 17, 2014 - 3:33:22 PM
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Achim Blumensath, David Janin. A syntactic congruence for languages of birooted trees. Semigroup Forum, Springer Verlag, 2014, 91 (3), pp.675-698. ⟨10.1007/s00233-014-9677-x⟩. ⟨hal-00947972⟩



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