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Lecture Notes in Computer Science
To reason effectively about programs, it is important to have some version of a transitive-closure operator so that we can describe such notions as the set of nodes reachable from a program's variables. On the other hand, with a few notable exceptions, adding transitive closure to even very tame logics makes them undecidable. In this paper, we explore the boundary between decidability and undecidability for transitive-closure logics. Rabin proved that the monadic second-order theory of trees isdoi:10.1007/978-3-540-30124-0_15 fatcat:udyjqmt67ff45bvtxf6l6fj47y