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The well known Hopcroft's algorithm to minimize deterministic completeautomata runs in $O(kn\log n)$-time, where $k$ is the size of the alphabet and$n$ the number of states. The main part of this algorithm corresponds to thecomputation of a coarsest bisimulation over a finite Deterministic LabelledTransition System (DLTS). By applying techniques we have developed in the caseof simulations, we design a new algorithm which computes the coarsestbisimulation over a finite DLTS in $O(m\log n)$-time and $O(k+m+n)$-space, with$m$ the number of transitions. The underlying DLTS does not need to be completeand thus: $m\leq kn$. This new algorithm is much simpler than the two othersfound in the literature.

Bisimulations over DLTS in O(m.log n)-time