In this paper the computational complexity of the (bi)simulation problem overrestricted graph classes is studied. For trees given as pointer structures orterms the (bi)simulation problem is complete for logarithmic space or NC$^1$,respectively. This solves an open problem from Balc'azar, Gabarr'o, andS'antha. Furthermore, if only one of the input graphs is required to be atree, the bisimulation (simulation) problem is contained in AC$^1$ (LogCFL). Incontrast, it is also shown that the simulation problem is P-complete alreadyfor graphs of bounded path-width.
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