The idea of synthesizing statecharts out of a collece tion of scenarios has received a lot of attention in ree cent years However due to the poor expr essive opwer of rst generation scenario languages including UML x sequence diagrams the propose d solutions often use ad hoc tricks and suer from many shortcomings The reecent adoption in UMLL of a richer scenario language including interesting composition operators now makes it possible to revisit the problem of statechart syntheesis with a radic ally new approach Inspir ed by the way UMLL sequence diagr ams can be algebraically come posed we rst de ne an algebraic framework for come posing state charts Then we show how to leverage the algebraic structure of UMLL sequence diagrams to get a direct algorithm for synthesizing a composition of state charts out of them.