BDD Algortihms and Cache Misses

Within the last few years, CPU speed has greatly overtaken memory speed. For this reason, implementation of symbolic algorithms— with their extensive use of pointers and hashing—must be reexamined. In this paper, we introduce the concept of cache miss complexity as an analytical tool for evaluating algorithms depending on pointer chasing. Such algorithms are typical of symbolic computation found in verification. We show how this measure suggests new data structures and algorithms for multi-terminal BDDs. Our ideas have been implemented in a BDD package, which is used in a decision procedure for the Monadic Second-order Logic on strings. Experimental results show that on large examples involving e.g the verification of concurrent programs, our implementation runs 4 to 5 times faster than a widely used BDD implementation. We believe that the method of cache miss complexity is of general interest to any implementor of symbolic algorithms used in verification.