Paolo Marin

sQueezeBF: an effective preprocessor for QBFs based on equivalence reasoning

In this paper we present sQueezeBF, an effective preprocessor for QBFs that combines various techniques for eliminating variables and/or redundant clauses. In particular sQueezeBF combines (i) variable elimination via Q-resolution, (ii) variable elimination via equivalence substitution and (iii) equivalence breaking via equivalence rewriting. The experimental analysis shows that sQueezeBF can produce significant reductions in the number of clauses and/or variables - up to the point that some instances are solved directly by sQueezeBF - and that it can significantly improve the efficiency of a range of state-of-the-art QBF solvers - up to the point that some instances cannot be solved without sQueezeBF preprocessing.

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.

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.

Incremental QBF preprocessing for partial design verification

Bounded Model Checking (BMC) is a major verification method for finding errors in sequential circuits. BMC accomplishes this by iteratively unfolding a circuit k times, adding the negated property, and finally converting the BMC instance into a sequence of satisfiability (SAT) problems. When considering incomplete designs (i.e. those containing so-called blackboxes), we rather need the logic of Quantified Boolean Formulas (QBF) to obtain a more precise modeling of the unknown behavior of the blackbox. Here, we answer the question of unrealizability of a property, where finding a path of length k proves that the property is violated regardless of the implementation of the blackbox. To boost this task, solving blackbox BMC problems incrementally has been shown to be feasible [3], although the restrictions required in the preprocessing phase reduce its effectiveness. In this paper we enhance the verification procedure when using an off-the-shelf QBF solver, through a stronger preprocessing of the QBF formulas applied in an incremental fashion.

HQSpre – An Effective Preprocessor for QBF and DQBF

We present our new preprocessor HQSpre, a state-of-the-art tool for simplifying quantified Boolean formulas (QBFs) and the first available preprocessor for dependency quantified Boolean formulas (DQBFs). The latter are a generalization of QBFs, resulting from adding so-called Henkin-quantifiers to QBFs. HQSpre applies most of the preprocessing techniques that have been proposed in the literature. It can be used both as a standalone tool and as a library. It is possible to tailor it towards different solver back-ends, e. g., to preserve the circuit structure of the formula when a non-CNF solver back-end is used. Extensive experiments show that HQSpre allows QBF solvers to solve more benchmark instances and is able to decide more instances on its own than state-of-the-art tools. The same impact can be observed in the DQBF domain as well.

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.

Verification of partial designs using incremental QBF

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, for some applications SAT formulas are not expressive enough, whereas a description via Quantified Boolean Formulas (QBF) is much more adequate, for instance when dealing with partial designs.Motivated by the success of incremental SAT, in this paper we explore various approaches to solve QBF problems in an incremental fashion and thereby make this technology usable as a core component of BMC. Firstly, we realized an incremental QBF solver based on the state-of-the-art QBF solver QuBE: Taking profit from the reuse of some information from previous iterations, the search space can be pruned, in some cases, to even less than a quarter.However, the need for preprocessing QBF formulas prior to the solving phase, that in general cannot be paired with incremental solving because of the non-predictable elimination of variables in the future incremental steps, posed the question of incremental QBF preprocessing. In this context we present an approach for retaining the QBF formula being preprocessed while extending its clauses and prefix incrementally. This procedure results in a significant size reduction of the QBF formulas, hence leading to a reduced solving time.As this may come together with a high preprocessing time, we analyze various heuristics to dynamically disable incremental preprocessing when its overhead raises over a certain threshold and is not compensated by the reduced solving time anymore.For proving the efficacy of our methods experimentally, as an application we consider BMC for partial designs (i.e., designs containing so-called blackboxes which represent unknown parts). Here, we disprove realizability, that is, we prove that an unsafe state is reachable no matter how the blackboxes are implemented. We examine all these incremental approaches from both the point of view of the effectiveness of the single procedure and the benefits that a range of QBF solvers can take from it. On a domain of partial design benchmarks, engaging incremental QBF methods significant performance gains over non incremental BMC can be achieved.

Comparison of knowledge sharing strategies in a parallel QBF solver

In this paper we examine the effect that different knowledge sharing strategies have on the performance of our parallel QBF Solver PaQuBE. This new Master/Slave MPI based solver leverages the additional computational power that can be exploited from modern computer and system architectures, to solve more relevant instances and faster than previous generation 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 that we optimize not only which information is shared, but how it is shared. In this context, we compare multiple conflict clause and solution cube sharing strategies, and finally show that an adaptive method works best. Additionally, compression of solution cubes was explored which reduced the system time associated with message passing while also reducing network traffic.