@article {IOPORT.01136647, author = {Kasangian, Stefano and Vigna, Sebastiano}, title = {The topos of labelled trees: A categorical semantics for SCCS.}, year = {1997}, journal = {Annales Societatis Mathematicae Polonae. Series IV}, volume = {32}, number = {1}, issn = {0169-2968}, pages = {27-45}, publisher = {IOS Press, Amsterdam}, abstract = {Summary: We give a semantics for SCCS using the constructions of the topos of labelled trees. The semantics accounts for all aspects of the original formulation of SCCS, including unbounded non-determinism. Then, a partial solution to the problem of characterizing bisimulation in terms of a class of morphisms is proposed. We define a class of morphisms of the topos of trees, called conflict preserving, such that two trees $T$ and $U$ are bisimilar iff there is a pair of conflict preserving morphisms $f: T\to U$ and $g:U\to T$ such that $fgf= f$ and $gfg= g$. It is the first characterization which does not require the existence of a third quotient object. The results can be easily extended to more general transition systems.}, identifier = {01136647}, }