Theoretical Foundations of Applied SAT Solving (14w5101)

Proving logic formulas is a problem of immense importance both theoretically and practically. On the one hand, it is believed to be intractable in general, and deciding whether this is so is one of the famous million dollar Clay Millennium Problems [20], namely the P vs. NP problem originating from the ground-breaking work of Cook [12]. On the other hand, today so-called SAT solvers based on conflict-driven clause learning (CDCL) [3, 18, 22] are routinely and successfully used to solve large-scale real-world instances in a wide range of application areas (such as hardware and software verification, electronic design automation, artificial intelligence research, cryptography, bioinformatics, operations research, and railway signalling systems, just to name a few examples — see, e.g., [8] for more details). During the last two decades, there have been dramatic — and surprising — developments in SAT solving technology that have improved performance by many orders of magnitude. But perhaps even more surprisingly, the best SAT solvers today are still at the core based on relatively simple methods from the early 1960s [14, 15] (albeit with many clever optimizations), searching for proofs in the so-called resolution proof system [9]. While such solvers can often handle formulas with millions of variables, there are also known tiny formulas with just a few hundred variables that cause even the very best solvers to stumble (see, e.g., theoretical work in [10, 17, 28] and experimental results in [19, 29]). The fundamental question of when SAT solvers perform well or badly, and what underlying mathematical properties of the formulas influence SAT solver performance, remains very poorly understood. Other crucial SAT solving issues, such as how to optimize memory management and how to exploit parallelization on modern multicore architectures, are even less well studied and understood from a theoretical point of view. Another intriguing fact is that although other mathematical methods of reasoning are known that are much stronger than resolution in theory, in particular methods based on algebra [11] and geometry [13], attempts to harness the power of such methods have conspicuously failed to deliver any significant improvements in practical performance. And while resolution is a fairly well-understood proof system, even very basic questions about these stronger algebraic and geometric methods remain wide open. The purpose of this workshop was to gather leading researchers in applied and theoretical areas of SAT and proof complexity research and to stimulate an increased exchange of ideas between these two communities. To the best of our knowledge, this was the first large-scale workshop aimed specifically at bringing together practitioners and theoreticians from the two fields. We believe that proof complexity can shed light