I'll talk about when BDD's are better than SAT, and discuss several attempts to improve on BDD's for symbolic model checking that met with limited success.

I will talk about my memories related to BDDs and ZDDs, starting from my first meeting with Randy.

Randy's style of practice-driven foundational research has inspired me through my career---I will share several cases of this starting with when I was a graduate student to later work on SAT solvers.

A brief retrospective of my experiences working with Randy with a particular focus on the birth of Symbolic Trajectory Evaluation.

In this short presentation I will describe how Bryant's classical 1986 paper has launched the knowledge-compilation revolution.

I will describe how decision diagrams can form the basis of a generic branch-and-bound method for discrete optimization. Using a state-based input model (e.g., a dynamic program), the method employs relaxed and restricted BDDs to provide optimization bounds. I will compare this approach to classical optimization methods such as integer programming and constraint programming.

Bryant's BDDs have had a tremendous impact in formal verification. In this talk, I will briefly describe how they have influenced my research across three decades in different domains of application, including our latest effort in verification of distributed systems.

The talk describes how z3 has used BDDs and ZDDs for solving EPR formulas, quantifier elimination, and manipulating polynomials. It also describes a journey in network verification tools using BDDs and related trie data-structures.

I was a graduate student at Carnegie Mellon when Randy arrive circa 1983. Both he and his work had a profound effect on my graduate experience and later career.

I will relate a few anecdotes about explorations at the intersection of machine learning, BDDs, and satisfiability solvers over the last 25 years.

For over four decades, I have helped develop tools that enable designers to create correct hardware and software systems. Some of these tools even claimed to provide formal guarantees of correctness. But they had a fundamental flaw—an error in an underlying algorithm or its implementation could cause the tool to produce an incorrect result. The prospects for developing efficient and scalable tools that are themselves formally verified seem unlikely. On the other hand, having tools produce checkable proofs of correctness yields nearly the same benefit. Even if the tool is buggy, each of its run can be formally verified. The SAT community instituted a requirement that solvers (at least those in the main track of the SAT competition) generate checkable proofs of unsatisfiability. This requirement has had a transformative effect on the quality of the solvers, the productivity of the developers, and the certainty of the competition results. We can learn from their experience in instituting this practice for other areas of automated reasoning.