  The rigorous theoretical analyses of algorithms for #SAT have been proposed
in the literature. As we know, previous algorithms for solving #SAT have been
analyzed only regarding the number of variables as the parameter. However, the
time complexity for solving #SAT instances depends not only on the number of
variables, but also on the number of clauses. Therefore, it is significant to
exploit the time complexity from the other point of view, i.e. the number of
clauses. In this paper, we present algorithms for solving #2-SAT and #3-SAT
with rigorous complexity analyses using the number of clauses as the parameter.
By analyzing the algorithms, we obtain the new worst-case upper bounds
O(1.1892m) for #2-SAT and O(1.4142m) for #3-SAT, where m is the number of
clauses.
