Over the last decade, research in the automatic synthesis and optimiza
tion of combinational logic has matured significantly; more recently,
research has focused on sequential logic. Many of the paradigms for co
mbinational logic have been extended and applied in the sequential dom
ain. In addition, promising new directions for future research are bei
ng explored. In this paper, we survey some of the results of combinati
onal synthesis and some recent results for sequential synthesis and th
en use these to view possible avenues for future sequential synthesis
research. In particular we look at two related questions: deriving a s
et of permissible behaviors and using a minimizer to select the best b
ehavior according to some optimization criteria. We examine these two
issues in increasingly complex situations starting with a single-outpu
t function, and proceeding to a single multiple-output function, a net
work of single-output functions, a network of multiple-output function
s, and then similar questions where ''function'' is replaced by a fini
te state machine (FSM). We end with a discussion of a network of finit
e state machines and the problem of deriving the set of permissible FS
M's and choosing a representative minimum one.