A Serverless Discrete Optimization Service in the Cloud Based on Boolean Circuit Satisfiability

Abstract

This thesis discusses the implementation of a serverless cloud service designed for solving discrete optimization problems encoded as boolean circuit satisfiability. Boolean circuit satisfiability problem involves determining whether an input assignment exists that satisfies a given boolean circuit. A cloud service is a platform that offers on-demand computing resources and services over the Internet. In a serverless setup, the service automatically manages and scales resources, eliminating the need for manual server management.

The main objective of this thesis is to provide a comprehensive and efficient approach to address problems in NP (nondeterministic polynomial time) by utilizing boolean circuit satisfiability. Our novel cloud service offers clients a more universal, efficient, and user-friendly solution for solving problems in NP.

We proposed an enhanced boolean logical circuit that incorporates sub-circuits capable of performing mathematical operations, simplifying the reduction process and expanding the potential to tackle problems in NP across various domains. Our motivation for this work arises from the fact that the augmented boolean circuit satisfiability problem is NP-complete, and a wide range of discrete optimization problems can be reduced to it. By leveraging a reduction to the proposed enhanced version of boolean circuit satisfiability problem and using oracles such as conjunctive normal form (CNF) or Integer Linear Programming (ILP) solvers, our service can efficiently address problems in NP in which the decision version can be reduced to the improved circuit satisfiability problems within polynomial time.

This thesis covers in-depth knowledge about the fundamentals of computational complexity, presenting reductions from each of Karp’s 21 NP-complete problems to the Circuit-SAT problem, demonstrating the versatility and applicability of our approach. Additionally, we discuss a software library we have built that enables the construction of circuits as well, allowing users to efficiently represent and solve problems using our cloud service. Furthermore, the thesis includes details about the service’s working principles and deployment aspects.