A global approach to the variable ordering problem in PSBDDs

We present a new global approach to the variable-ordering problem in Pseudo-Symmetric Binary Decision Diagrams (PSBDDs). It is based on analyzing symmetric relations between functions´ variables. We group all function´s variables into symmetry chains and then order the chains based on symmetries. To further reduce the size and the number of levels in PSBDDs, we introduce a hierarchical decomposition method, based on multiple symmetries. Comparing to the previously published results, we substantially reduced the numbers of levels (delay) in PSBDDs, and for many non-symmetric benchmark functions we did not have to use any repeated variables. Results for MCNC benchmark functions are presented