Abstract
We express conditions for a term to be a finite grid-like structure. Together with definitions of term properties by excluding “forbidden patterns” we obtain three new undecidability results in three areas: the ∃*∀*-fragment of the theory of one-step rewriting for linear and shallow rewrite systems, the emptiness for automata with equality tests between first cousins (i.e. only tests at depth 2 below the current node are available), and the ∃*∀*-fragment of the theory of set constraints.
Partially supported by The Esprit working group CCL II (22457) and the HCM project CONSOLE (CHRXCT940495)
Partially supported by “GDR AMI” Groupement De Recherche 1116 du CNRS
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Seynhaeve, F., Tommasi, M., Treinen, R. (1997). Grid structures and undecidable constraint theories. In: Bidoit, M., Dauchet, M. (eds) TAPSOFT '97: Theory and Practice of Software Development. CAAP 1997. Lecture Notes in Computer Science, vol 1214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030610
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