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Abstract:
We show that rigid reachability, the non-symmetric form of rigid
E-unification, is undecidable already in the case of a single
constraint. From this we infer the undecidability of a new
rather restricted kind of second-order unification.
We also show that certain decidable subclasses of the problem
which are PTIME-complete in the equational case
become EXPTIME-complete when symmetry is absent.
By applying automata-theoretic methods,
simultaneous monadic rigid reachability with ground rules
is shown to be in EXPTIME.
