Symbolic representation with ordered function templates

Abstract

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.interest. Edge attributes further reduce the size requirements. In [10], the authors proposed three edge-attributes to reduce the size of the shared DAG:

Improving BDD Based Symbolic Model Checking with Isomorphism Exploiting Transition Relations

“…These papers just present approaches for identity reduction, but no method to use similarities in the transition relations of components. A technique to exploit sharing in BDDs for regular circuits that differ only in their support variables has been presented in [9]. Similar to our approach a remapping of input variables is used there.…”