In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP). Concretely, we prove that polynomial-sized message-passing algorithms can represent the most powerful polynomial time algorithms for Max Constraint Satisfaction Problems assuming the Unique Games Conjecture. We leverage this result to construct efficient graph neural network architectures, OptGNN, that obtain high quality approximate solutions on landmark combinatorial optimization problems such as Max-Cut, Min-Vertex-Cover, and Max-3-SAT. Our approach achieves strong empirical results across a wide range of real-world and synthetic datasets against solvers and neural baselines. Finally, we take advantage of OptGNN’s ability to capture convex relaxations to design an algorithm for producing bounds on the optimal solution from the learned embeddings of OptGNN.

The end of Moore’s Law has ushered in a diversity of hardware not seen in decades. Operating system (OS) (and system software) portability is accordingly becoming increasingly critical. Simultaneously, there has been tremendous progress in program synthesis. We set out to explore the feasibility of using modern program synthesis to generate the machine-dependent parts of an operating system. Our ultimate goal is to generate new ports automatically from descriptions of new machines. One of the issues involved is writing specifications, both for machine-dependent operating system functionality and for instruction set architectures. We designed two domain-specific languages: Alewife for machine-independent specifications of machine-dependent operating system functionality and Cassiopea for describing instruction set architecture semantics. Automated porting also requires an implementation. We developed a toolchain that, given an Alewife specification and a Cassiopea machine description, specializes the machine-independent specification to the target instruction set architecture and synthesizes an implementation in assembly language with a customized symbolic execution engine. Using this approach, we demonstrate the successful synthesis of a total of 140 OS components from two pre-existing OSes for four real hardware platforms. We also developed several optimization methods for OS-related assembly synthesis to improve scalability. The effectiveness of our languages and ability to synthesize code for all 140 specifications is evidence of the feasibility of program synthesis for machine-dependent OS code. However, many research challenges remain; we also discuss the benefits and limitations of our synthesis-based approach to automated OS porting.

Recent advances in program synthesis convinced us that it was the right time to transform the process of porting an operating system into a program synthesis problem. We set out to synthesize the needed machine dependent code for an existing operating system. This undertaking proved far more challenging than we anticipated. We summarize our experience and lessons learned and propose next steps in realizing such an undertaking.