  A recently proposed canonical form of Boolean functions, namely tagged
sentential decision diagrams (TSDDs), exploits both the standard and
zero-suppressed trimming rules. The standard ones minimize the size of
sentential decision diagrams (SDDs) while the zero-suppressed trimming rules
have the same objective as the standard ones but for zero-suppressed sentential
decision diagrams (ZSDDs). The original TSDDs, which we call zero-suppressed
TSDDs (ZTSDDs), firstly fully utilize the zero-suppressed trimming rules, and
then the standard ones. In this paper, we present a variant of TSDDs which we
call standard TSDDs (STSDDs) by reversing the order of trimming rules. We then
prove the canonicity of STSDDs and present the algorithms for binary operations
on TSDDs. In addition, we offer two kinds of implementations of STSDDs and
ZTSDDs and acquire three variations of the original TSDDs. Experimental
evaluations demonstrate that the four versions of TSDDs have the size advantage
over SDDs and ZSDDs.
