Matthew D. T. Lewis

Multithreaded SAT Solving

This paper describes the multithreaded MiraXT SAT solver which was designed to take advantage of current and future shared memory multiprocessor systems. The paper highlights design and implementation details that allow the multiple threads to run and cooperate efficiently. Results show that in single threaded mode, MiraXT compares well to other state of the art solvers on industrial problems. In threaded mode, it provides cutting edge performance, as speedup is obtained on both SAT and UNSAT instances.

Thread-Parallel Integrated Test Pattern Generator Utilizing Satisfiability Analysis

Efficient utilization of the inherent parallelism of multi-core architectures is a grand challenge in the field of electronic design automation (EDA). One EDA algorithm associated with a high computational cost is automatic test pattern generation (ATPG). We present the ATPG tool TIGUAN based on a thread-parallel SAT solver. Due to a tight integration of the SAT engine into the ATPG algorithm and a carefully chosen mix of various optimization techniques, multi-million-gate industrial circuits are handled without aborts. TIGUAN supports both conventional single-stuck-at faults and sophisticated conditional multiple stuck-at faults which allows to generate patterns for non-standard fault models. We demonstrate how TIGUAN can be combined with conventional structural ATPG to extract full benefit of the intrinsic strengths of both approaches.

Incremental preprocessing methods for use in BMC

Traditional incremental SAT solvers have achieved great success in the domain of Bounded Model Checking (BMC). Recently, modern solvers have introduced advanced preprocessing procedures that have allowed them to obtain high levels of performance. Unfortunately, many preprocessing techniques such as variable and (blocked) clause elimination cannot be directly used in an incremental manner. This work focuses on extending these techniques and Craig interpolation so that they can be used effectively together in incremental SAT solving (in the context of BMC). The techniques introduced here doubled the performance of our BMC solver on both SAT and UNSAT problems. For UNSAT problems, preprocessing had the added advantage that Craig interpolation was able to find the fixed point sooner, reducing the number of incremental SAT iterations. Furthermore, our ideas seem to perform better as the benchmarks become larger, and/or deeper, which is exactly when they are needed. Lastly, our methods can be integrated into other SAT based BMC tools to achieve similar speedups.

PaMira - A Parallel SAT Solver with Knowledge Sharing

In this paper we describe PaMira, a powerful distributed SAT solver. PaMira is based on the highly optimized, sequential SAT engine Mira, incorporating all essential optimization techniques modern algorithms utilize to maximize performance. For the distributed execution an efficient work stealing method has been implemented. PaMira also employs the exchange of conflict clauses between the processes to guide the search more efficiently. We provide experimental results showing linear speedup on a multiprocessor environment with four AMD Opteron processors

TIGUAN: Thread-Parallel Integrated Test Pattern Generator Utilizing Satisfiability ANalysis

We present the automatic test pattern generator TIGUAN based on a thread-parallel SAT solver. Due to a tight integration of the SAT engine into the ATPG algorithm and a carefully chosen mix of various optimization techniques, multi-million-gate industrial circuits are handled without aborts. TIGUAN supports both conventional single-stuck-at faults and sophisticated conditional multiple stuck-at faults which allows to generate patterns for non-standard fault models.

Verification of partial designs using incremental QBF solving

SAT solving is an indispensable core component of numerous formal verification tools and has found widespread use in industry, in particular when using it in an incremental fashion, e.g. in Bounded Model Checking (BMC). On the other hand, there are applications, in particular in the area of partial design verification, where SAT formulas are not expressive enough and a description via Quantified Boolean Formulas (QBF) is much more adequate. In this paper we introduce incremental QBF solving and thereby make it usable as a core component of BMC. To do so, we realized an incremental version of the state-of-the-art QBF solver QuBE, allowing for the reuse of learnt information e.g. in the form of conflict clauses and solution cubes. As an application we consider BMC for partial designs (i.e. designs containing so-called blackboxes) and thereby disprove realizability, that is, we prove that an unsafe state is reachable no matter how the blackboxes are implemented. In our experimental analysis, we compare different incremental approaches implemented in our BMC tool. BMC with incremental QBF turns out to be feasible for designs with more than 21,000 gates and 2,700 latches. Significant performance gains over non incremental QBF based BMC can be obtained on many benchmark circuits, in particular when using the so-called backward-incremental approach combined with incremental preprocessing.

Encoding techniques, craig interpolants and bounded model checking for incomplete designs

This paper focuses on bounded invariant checking for partially specified circuits – designs containing so-called blackboxes – using the well known 01X- and QBF-encoding techniques. For detecting counterexamples, modeling the behavior of a blackbox using 01X-encoding is fast, but rather coarse as it limits what problems can be verified. We introduce the idea of 01X-hardness, mainly the classification of problems for which this encoding technique does not provide any useful information about the existence of a counterexample. Furthermore, we provide a proof for 01X-hardness based on Craig interpolation, and show how the information contained within the Craig interpolant or unsat-core can be used to determine heuristically which blackbox outputs to model in a more precise way. We then compare 01X, QBF and multiple hybrid modeling methods. Finally, our total workflow along with multiple state-of-the-art QBF-solvers are shown to perform well on a range of industrial blackbox circuit problems.

PaQuBE: Distributed QBF Solving with Advanced Knowledge Sharing

In this paper we present the parallel QBF Solver PaQuBE . This new solver leverages the additional computational power that can be exploited from modern computer architectures, from pervasive multicore boxes to clusters and grids, to solve more relevant instances and faster than previous generation solvers. PaQuBE extends QuBE , its sequential core, by providing a Master/Slave Message Passing Interface (MPI) based design that allows it to split the problem up over an arbitrary number of distributed processes. Furthermore, PaQuBE s progressive parallel framework is the first to support advanced knowledge sharing in which solution cubes as well as conflict clauses can be shared. According to the last QBF Evaluation, QuBE is the most powerful state-of-the-art QBF Solver. It was able to solve more than twice as many benchmarks as the next best independent solver. Our results here, show that PaQuBE provides additional speedup, solving even more instances, faster.

Speedup techniques utilized in modern SAT solvers

This paper describes and compares features and techniques modern SAT solvers utilize to maximize performance. Here we focus on: Implication Queue Sorting (IQS) combined with Early Conflict Detection Based BCP (ECDB); and a modified decision heuristic based on the combination of Variable State Independent Decaying Sum (VSIDS), Berkmin, and Sieges Variable Move to Front (VMTF). These features were implemented and compared within the framework of the MIRA SAT solver. The efficient implementation and analysis of these features are presented and the speedup and robustness each feature provides is demonstrated. Finally, with everything enabled (ECDB with IQS and advanced decision heuristics), MIRA was able to consistently outperform zChaff and even Forklift on the benchmarks provided, solving 37 out of 111 industrial benchmarks compared to zChaffs 21 and Forklifts 28.

Parallel QBF Solving with Advanced Knowledge Sharing

In this paper we present the parallel QBF Solver PaQuBE. This new solver leverages the additional computational power that can be exploited from modern computer architectures, from pervasive multi-core boxes to clusters and grids, to solve more relevant instances faster than previous generation solvers. Furthermore, PaQuBEs progressive MPI based parallel framework is the first to support advanced knowledge sharing in which solution cubes as well as conflict clauses can be exchanged between solvers. Knowledge sharing plays a critical role in the performance of PaQuBE. However, due to the overhead associated with sending and receiving MPI messages, and the restricted communication/network bandwidth available between solvers, it is essential to optimize not only what information is shared, but the way in which it is shared. In this context, we compare multiple conflict clause and solution cube sharing strategies, and finally show that an adaptive method provides the best overall results.