Lower bounds for acyclic string constraints under concatenation-only relational constraints

Ascertain whether the NEXPTIME lower bounds established for satisfiability of the acyclic fragment of string constraints with subword-ordering and shuffle in Aiswarya–Mal–Saivasan (LICS 2022) continue to hold when shuffle is replaced by concatenation; equivalently, prove or refute that the satisfiability problem for the acyclic concatenation-only fragment (without rational transductions) is NEXPTIME-hard.

Background

The earlier work [9] proved NEXPTIME-completeness for acyclic string constraints using subword-ordering with shuffle and regular/context-free membership, but did not treat the concatenation-only variant. This paper shows that in its own transducer-augmented model, their hardness results persist even when shuffle (and even concatenation) is disallowed, because their reduction uses only single-variable right-hand sides.

However, for the original no-transducer model of [9], whether the same lower bounds apply when restricting relational constraints to concatenation only remains unresolved. Establishing or refuting NEXPTIME-hardness for this acyclic concatenation-only fragment is therefore an explicit open problem.