Symbolic representation with ordered function templates

Binary Decision Diagrams (BDDs) often fail to exploit sharing between Boolean functions that differ only in their support variables. In a memory circuit, for example, the functions for the different bits of a word differ only in the data bit while the address decoding part of the function is identical. We present a symbolic representation approach using ordered function templates to exploit such regularity. Templates specify functionality without being bound to a specific set of variables. Functions are obtained by instantiating templates with a list of variables. We ensure canonicity of the representation by requiring that templates are normalized and argument lists are ordered. We also present algorithms for performing Boolean operations using this representation. Experiments with a prototype implementation built on top of CUDD indicate that function templates can dramatically reduce memory requirements for symbolic simulation of regular circuits.