Abstract
A transformation of structures τ is monadic second-order compatible (MS-compatible) if every monadicsec ond-order property P can be effectively rewritten into a monadic second-order property Q such that, for every structure S, if T is the transformed structure τ (S), then P(T) holds i. Q(S) holds.
We will review Monadic Second-order definable transductions (MS-transductions): they are MS-compatible transformations of a particular form, i.e., defined by monadicsec ond-order (MS) formulas.
The unfolding of a directed graph into a tree is an MS-compatible transformation that is not an MS-transduction.
The MS-compatibility of various transformations of semantical interest follows. We will present three main cases and discuss applications and open problems.
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Courcelle, B. (2002). Semantical Evaluations as Monadic Second-Order Compatible Structure Transformations. In: Nielsen, M., Engberg, U. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2002. Lecture Notes in Computer Science, vol 2303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45931-6_1
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DOI: https://doi.org/10.1007/3-540-45931-6_1
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