Functional Synthesis: An Ideal Meeting Ground for Formal Methods and Machine Learning

Kuldeep Meel
National University of Singapore


Don’t we all dream of the perfect assistant whom we can just tell what to do and the assistant can figure out how to accomplish the tasks? Formally, given a specification F(X,Y) over the set of input variables X and output variables Y, we want the assistant, aka functional synthesis engine, to design a function G such that F(X,G(X)) is true. Functional synthesis has been studied for over 150 years, dating back Boole in 1850’s and yet scalability remains a core challenge. Motivated by progress in machine learning, we design a new algorithmic framework Manthan, which views functional synthesis as a classification problem, relying on advances in constrained sampling for data generation, and advances in automated reasoning for a novel proof-guided refinement and provable verification. On an extensive and rigorous evaluation over 609 benchmarks, we demonstrate that Manthan significantly improves upon the current state of the art, solving 356 benchmarks in comparison to 280, which is the most solved by a state of the art technique; thereby, we demonstrate an increase of 76 benchmarks over the current state of the art. The significant performance improvements call for interesting future work at the intersection of machine learning, constrained sampling, and automated reasoning.


Kuldeep Meel is the Sung Kah Kay Assistant Professor in the Computer Science Department of School of Computing at the National University of Singapore. His research interests lie at the intersection of Formal Methods and Artificial Intelligence. He is a recipient of 2019 NRF Fellowship for AI (accompanied with 2.5 million SGD funding), and was named AI’s 10 to Watch by IEEE Intelligent Systems in 2020. His work received the 2018 Ralph Budd Award for Best PhD Thesis in Engineering, 2014 Outstanding Masters Thesis Award from Vienna Center of Logic and Algorithms and Best Student Paper Award at CP 2015. He received his Ph.D. (2017) and M.S. (2014) degree from Rice University, and B. Tech. (with Honors) degree (2012) in Computer Science and Engineering from Indian Institute of Technology, Bombay.