Effective construction of the syntactic algebra of a recognizable series on trees
Abstract
In this paper we exhibit two different effective constructions of the syntactic algebra A _{ S } associated to a recognizable formal series on trees S. The one method consists of a direct construction of [Figure not available: see fulltext.] (=a copy of A _{ S }) which is the subspace [Figure not available: see fulltext.] with the natural algebra structure. We first determine a basis [Figure not available: see fulltext.] of the subspace [Figure not available: see fulltext.] and then, using the junction isomorphism [Figure not available: see fulltext.] we obtain a basis for[Figure not available: see fulltext.]. The second method consists of considering an arbitrary surjective realization ( A, φ) of S, defining an appropriate ideal ℬ of A and then constructing the quotient algebra A/ℬ this quotient is isomorphic to A _{ S } and thus independent of the choice of ( A _{ S } φ).
 Publication:

International Journal of Biometeorology
 Pub Date:
 December 1992
 DOI:
 10.1007/BF01212960
 Bibcode:
 1992IJBm...36..351B