Lowerbounds for Bisimulation by Partition Refinement

We provide time lower bounds for sequential and parallel algorithms deciding bisimulation on labeled transition systems that use partition refinement. For this is $\Omega((m \mkern1mu {+} n ) \mkern-1mu \log n)$ $\Omega(n)$, where $n$ the number of states $m$ transitions. The lowerbounds are obtained by analysing families deterministic systems, ultimately with two actions in case, one action algorithms. action, bisimilarity can be decided sequentially fundamentally different techniques than In particular, Paige, Tarjan, Bonic give a linear algorithm specific situation. show, exploiting concept an oracle, approach not help to develop faster generic bisimilarity. there similar situation these may applied, too.