Exploiting Satisfiability Solvers for Efficient Logic Synthesis

Logic synthesis is an important part of electronic design automation (EDA) flows, which enable the implementation of digital systems. As the design size and complexity increase, the data structures and algorithms for logic synthesis must adapt and improve in order to keep pace and to maintain acceptable runtime and high-quality results. Large circuits were often represented using binary decision diagrams (BDDs) that were rapidly adopted by logic synthesis tools beginning in the 1980s. Nowadays, BDD-based algorithms are still enhanced, but the possibilities for improvement are somewhat saturated after some 35 years of research. Alternatively, the first EDA applications that exploit Boolean satisfiability (SAT) were developed in the 1990s. Despite the worst-case exponential runtime of SAT solvers, rapid progress in their performance enabled the creation of efficient SAT-based algorithms. Yet, logic synthesis started using SAT solvers more diffusely only in the last decade. Therefore, thorough research is still required both for exploiting SAT solvers and for encoding logic synthesis problems into SAT. Our main goal in this thesis is to facilitate and promote the further integration of SAT solvers into EDA by proposing and evaluating novel SAT-based algorithms that can be used as building blocks in logic synthesis tools. First, we propose a rapid algorithm for LEXSAT, which generates satisfying assignments in lexicographic order. We show that LEXSAT can bring canonicity, which guarantees the generation of unique results, when using SAT solvers in EDA applications. Next, we present a new SAT-based algorithm that progressively generates irredundant sums of products (SOPs), which still play a crucial role in many logic synthesis tools. Using LEXSAT, for the first time, we can generate canonical SAT-based SOPs that, much like BDD-based SOPs, are unique for a given function and variable order but could relax canonicity in order to improve speed and scalability. Unlike BDDs, due to its progressive nature, our algorithm can generate partial SOPs for applications that can work with incomplete circuit functionality. It is noteworthy that both LEXSAT and the SAT-based SOPs are applicable beyond logic synthesis and EDA. Finally, we focus on resubstitution, which reimplements a given Boolean function as a new function that depends on a set of existing functions called divisors. We propose the carving interpolation algorithm that, unlike the traditional Craig interpolation, forces the use of a specific divisor as an input of the new function. This is particularly useful for global circuit restructuring and for some synthesis-based engineering change order (ECO) algorithms. Furthermore, we compare two existing SAT-based methodologies for resubstitution, which are used for post-mapping logic optimisation. The first methodology combines SAT-based functional dependency checking and Craig interpolation that are also used for our carving interpolation; the second methodology is based on cube enumeration and is similar to the SAT-based SOP generation. The initial implementations of our novel SAT-based algorithms offer either better performance or new features, or both, compared to their state-of-the-art versions. As the results indicate, a further thorough development of SAT-based algorithms for logic synthesis, like the one performed for BDDs in the past, can help overcome existing limitations and keep up with growing designs and design complexity

Almost Symmetries and the Unit Commitment Problem

This thesis explores two main topics. The first is almost symmetry detection on graphs. The presence of symmetry in combinatorial optimization problems has long been considered an anathema, but in the past decade considerable progress has been made. Modern integer and constraint programming solvers have automatic symmetry detection built-in to either exploit or avoid symmetric regions of the search space. Automatic symmetry detection generally works by converting the input problem to a graph which is in exact correspondence with the problem formulation. Symmetry can then be detected on this graph using one of the excellent existing algorithms; these are also the symmetries of the problem formulation.The motivation for detecting almost symmetries on graphs is that almost symmetries in an integer program can force the solver to explore nearly symmetric regions of the search space. Because of the known correspondence between integer programming formulations and graphs, this is a first step toward detecting almost symmetries in integer programming formulations. Though we are only able to compute almost symmetries for graphs of modest size, the results indicate that almost symmetry is definitely present in some real-world combinatorial structures, and likely warrants further investigation.The second topic explored in this thesis is integer programming formulations for the unit commitment problem. The unit commitment problem involves scheduling power generators to meet anticipated energy demand while minimizing total system operation cost. Today, practitioners usually formulate and solve unit commitment as a large-scale mixed integer linear program.The original intent of this project was to bring the analysis of almost symmetries to the unit commitment problem. Two power generators are almost symmetric in the unit commitment problem if they have almost identical parameters. Along the way, however, new formulations for power generators were discovered that warranted a thorough investigation of their own. Chapters 4 and 5 are a result of this research.Thus this work makes three contributions to the unit commitment problem: a convex hull description for a power generator accommodating many types of constraints, an improved formulation for time-dependent start-up costs, and an exact symmetry reduction technique via reformulation

Workshop Notes of the Sixth International Workshop "What can FCA do for Artificial Intelligence?"

International audienc

Progressive Generation of Canonical Irredundant Sums of Products Using a SAT Solver

International audienceWe present an algorithm that progressively generates canonical irredun-dant Sums Of Products (SOPs) for completely-and incompletely-specified Boolean functions using a satisfiability (SAT) solver. The progressive generation allows for real time monitoring and early termination, as well as for generation of partial SOPs for incremental applications. On the other hand, canonicity brings independence of the original representation and often yields smaller and more regular SOPs that lead to smaller circuits after algebraic factoring. Also, canonicity is key in applications such as constraint solving and random assignment generation, which traditionally rely on methods based on Binary Decision Diagram (BDD). However, in contrast with BDDs, our algorithm can relax canonicity to improve speed and scalability. In general, our method is more scalable for benchmarks with many structurally isomor-phic outputs. It also improves the quality of results up to 10%, in terms of the SOP size, compared to a state-of-the-art BDD-based method. Experiments with global circuit restructuring using SAT-based SOPs show that area-delay product can be improved up to 27%, compared to global restructuring using BDD-based SOPs

Новые информационные технологии в исследовании сложных структур : материалы Тринадцатой международной конференции, 7-9 сентября 2020 г

Тринадцатая конференция с международным участием «Новые информационные технологии в исследовании сложных структур» была проведена в дистанционном формате с 7 по 9 сентября 2020 г. Материалы сборника ориентированы на использование специалистами в области информационных технологий в различных сферах человеческой деятельности, включая вычислительные и телекоммуникационные системы, образование, архитектуру и градостроительство, охрану природы, здравоохранение, разработку систем искусственного интеллекта, исследование дискретных и стохастических структур управления и связи