  Algorithms which compute the coarsest simulation preorder are generally
designed on Kripke structures. Only in a second time they are extended to
labelled transition systems. By doing this, the size of the alphabet appears in
general as a multiplicative factor to both time and space complexities. Let $Q$
denotes the state space, $\rightarrow$ the transition relation, $\Sigma$ the
alphabet and $P_{sim}$ the partition of $Q$ induced by the coarsest simulation
equivalence. In this paper, we propose a base algorithm which minimizes, since
the first stages of its design, the incidence of the size of the alphabet in
both time and space complexities. This base algorithm, inspired by the one of
Paige and Tarjan in 1987 for bisimulation and the one of Ranzato and Tapparo in
2010 for simulation, is then derived in three versions. One of them has the
best bit space complexity up to now,
$O(|P_{sim}|^2+|{\rightarrow}|.\log|{\rightarrow}|)$, while another one has the
best time complexity up to now, $O(|P_{sim}|.|{\rightarrow}|)$. Note the
absence of the alphabet in these complexities. A third version happens to be a
nice compromise between space and time since it runs in
$O(b.|P_{sim}|.|{\rightarrow}|)$ time, with $b$ a branching factor generally
far below $|P_{sim}|$, and uses
$O(|P_{sim}|^2.\log|P_{sim}|+|{\rightarrow}|.\log|{\rightarrow}|)$ bits.
