Polynomial Formal Verification: Ensuring Correctness under Resource Constraints : (Invited Paper)

Recently, a lot of effort has been put into developing formal verification approaches by both academic and industrial research. In practice, these techniques often give satisfying results for some types of circuits, while they fail for others. A major challenge in this domain is that the verification techniques suffer from unpredictability in their performance. The only way to overcome this challenge is the calculation of bounds for the space and time complexities. If a verification method has polynomial space and time complexities, scalability can be guaranteed.In this tutorial paper, we review recent developments in formal verification techniques and give a comprehensive overview of Polynomial Formal Verification (PFV). In PFV, polynomial upper bounds for the run-time and memory needed during the entire verification task hold. Thus, correctness under resource constraints can be ensured. We discuss the importance and advantages of PFV in the design flow. Formal methods on the bit-level and the word-level, and their complexities when used to verify different types of circuits, like adders, multipliers, or ALUs are presented. The current status of this new research field and directions for future work are discussed.