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Abstract:
In this paper we prove decidability results of restricted
fragments of simultaneous rigid reachability or SRR, that
is the nonsymmetrical form of simultaneous rigid E-unification
or SREU. The absence of symmetry forces us to use different
methods, from the ones that have been successful in the context
of SREU in the past (for example word equations). 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. The first result indicates
the difference in computational 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.
