CFLOBDDs: Context-Free-Language Ordered Binary Decision Diagrams

Abstract

This paper presents a new compressed representation of Boolean functions, called CFLOBDDs (for Context-Free-Language Ordered Binary Decision Diagrams). They are essentially a plug-compatible alternative to BDDs (Binary Decision Diagrams), and hence useful for representing certain classes of functions, matrices, graphs, relations, etc. in a highly compressed fashion. CFLOBDDs share many of the good properties of BDDs, but—in the best case—the CFLOBDD for a Boolean function can be exponentially smaller than any BDD for that function. Compared with the size of the decision tree for a function, a CFLOBDD—again, in the best case—can give a double-exponential reduction in size. They have the potential to permit applications to (i) execute much faster, and (ii) handle much larger problem instances than has been possible heretofore.

We applied CFLOBDDs in quantum-circuit simulation, and found that for several standard problems the improvement in scalability, compared to BDDs, is quite dramatic. With a 15-minute timeout, the number of qubits that CFLOBDDs can handle are 65,536 for GHZ, 524,288 for BV; 4,194,304 for DJ; and 4,096 for Grover’s Algorithm, besting BDDs by factors of 128 ×, 1,024 ×, 8,192 ×, and 128 ×, respectively.