The complexity of admissible rules of {L}ukasiewicz logic

We investigate the computational complexity of admissibility of inference rules in infinite-valued {\L}ukasiewicz propositional logic (\L). It was shown in [13] that admissibility in {\L} is checkable in PSPACE. We establish that this result is optimal, i.e., admissible rules of {\L} are PSPACE-complete. In contrast, derivable rules of {\L} are known to be coNP-complete.