Computing by splicing is a new powerful tool stemming originally from
molecular genetics. This new model of computing, splicing systems, is
investigated here. Several variants, resulting from the use of the rul
es in different ways, are considered. The power of such systems with v
ery weak structure imposed on rules turns out to be very large. Charac
terizations of recursively enumerable languages are obtained for many
variants. In this way our study is analogous to the early studies conc
erning variations of Turing machines. Other classes of such splicing s
ystems generate only regular or context-free languages (giving, in fac
t, characterizations of these families). With a few exceptions, we are
able to obtain precise characterizations for all resulting families.