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We note that the remarkable EXPSPACE-hardness result in [G\"oller, Haase,Ouaknine, Worrell, ICALP 2010] ([GHOW10] for short) allows us to answer an opencomplexity question for simulation preorder of succinct one counter nets (i.e.,one counter automata with no zero tests where counter increments and decrementsare integers written in binary). This problem, as well as bisimulationequivalence, turn out to be EXPSPACE-complete. The technique of [GHOW10] wasreferred to by Hunter [RP 2015] for deriving EXPSPACE-hardness of reachabilitygames on succinct one-counter nets. We first give a direct self-containedEXPSPACE-hardness proof for such reachability games (by adjusting a knownPSPACE-hardness proof for emptiness of alternating finite automata withone-letter alphabet); then we reduce reachability games to (bi)simulation gamesby using a standard "defender-choice" technique.

EXPSPACE-hardness of behavioural equivalences of succinct one-counter nets