Transforming structures by set interpretations

Thomas Colcombet (1) , Christof Löding (2)

1 GALION - Graphs, Automata, Logics, Languages and vErificatiON
2 RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University

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.

Mots clés: Monadic Logic; First-order logic; Logic interpretations; Infinite structures; Automatic structures

Domaines: Logique en informatique [cs.LO]

Thomas Colcombet, Christof Löding. Transforming structures by set interpretations. Logical Methods in Computer Science, 2007, 3 (2), paper 4. ⟨10.2168/LMCS-3(2:4)2007⟩. ⟨hal-00192051⟩