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.