Robustness of PSPACE-complete sets

We study the robustness of complete languages in PSPACE and prove that they are robust against P-selective sparse sets. Earlier similar results are known for EXP-complete sets [H. Buhrman, A. Hoene, L. Torenvliet, Splittings, robustness, and structure of complete sets, SIAM J. Comput. 27 (3) (1998) 637-653] and NP-complete sets [C. Glaszer, A. Pavan, A. Selman, S. Sengupta, Properties of NP-complete sets, in: IEEE Conference on Computational Complexity, 2004, pp. 184-197].

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