Decidable fragments of simultaneous rigid reachability

Abstract

In this paper we prove decidability results of restricted frag- ments of simultaneous rigid reachability or SRR, that is the nonsymme- Trical form of simultaneous rigid E-unification or SREU. The absence of symmetry enforces us to use different methods, than the ones that have been successful in the context of SREU (for example word equati- ons). The methods that we use instead, involve finite (tree) automata techniques, and the decidability proofs provide precise computational complexity bounds. The main results are 1) monadic SRR with ground rules is PSPACE-complete, and 2) balanced SRR with ground rules is EXPTIME-complete. These upper bounds have been open already for corresponding fragments of SREU, for which only the hardness results have been known. The first result indicates the difference in computatio- nal power between fragments of SREU with ground rules and nonground rules, respectively, due to a straightforward encoding of word equations in monadic SREU (with nonground rules). The second result establishes the decidability and precise complexity of the largest known subfragment of nonmonadic SREU. © Springer-Verlag Berlin Heidelberg 1999.