Transforming structures by set interpretations

Details Transforming structures by set interpretations Transforming structures by set interpretations

2007-03-08

arxiv.org/abs/cs/0703039v2

LMCS 3 (2:4) 2007

Computer Science

Logic in Computer Science

36 pages

Scientific paper

10.2168/LMCS-3(2:4)2007

We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.

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