On the sensitivity of BDDs with respect to path-related objective functions

Reduced ordered binary decision diagrams (BDDs) are a data structure for efficient representation and manipulation of Boolean functions. They are frequently used in logic synthesis and formal verification. In recent practical applications, BDDs are optimized with respect to new objective functions. In 1986, Bryant showed that, dependent on a chosen variable ordering, the size of BDDs can vary from linear to exponential. In this paper, we derive similar results for the sensitivity of BDDs with respect to path-related objective functions. First, we provide a theoretical view, giving examples for the large variation in the maximal path length and the expected path length in BDDs. This shows how important it is to choose a good or optimal variable ordering. Experimental results show the sensitivity of benchmark functions with respect to all considered objective functions