Martina Seidl’s research while affiliated with Johannes Kepler University of Linz and other places

Symmetries have been exploited successfully within the realms of SAT and QBF to improve solver performance in practical applications and to devise more powerful proof systems. As a first step towards extending these advancements to the class of dependency quantified Boolean formulas (DQBFs), which generalize QBF by allowing more nuanced variable dependencies, this work develops a comprehensive theory to characterize symmetries for DQBFs. We also introduce the notion of symmetry breakers of DQBFs, along with a concrete construction, and discuss how to detect DQBF symmetries algorithmically using a graph-based approach.

We lift the problem of enumerative solution counting to quantified Boolean formulas (QBFs) at the second quantifier block. In contrast to the well-explored model counting problem for SAT (#SAT), where models are simply assignments to the Boolean variables of a formula, we are now dealing with tree (counter-)models reflecting the dependencies between the variables of the first and the second quantifier block. It turns out that enumerative counting on the second level does not give the complete solution count and more fine-grained view is necessary. We present a level-2 solution counting approach that works for true and false formulas. We implemented the presented approach in a counting tool exploiting state-of-the-art QBF solving technology. We present several kinds of benchmarks for testing our implementation and show that even with this very basic approach of solution enumeration the solution counts of challenging benchmarks can be found.

This paper addresses the challenge of solution counting for Quantified Boolean Formulas (QBFs), a task distinct from the well-established model counting problem for SAT (\#SAT). Unlike SAT, where models are straightforward assignments to Boolean variables, QBF solution counting involves tree models that capture dependencies among variables within different quantifier blocks. We present a comprehensive top-down tree model counter capable of handling diverse satisfiable QBF formulas. Emphasizing the critical role of the branching heuristic, which must consider variables in the correct order according to quantification blocks, we further demonstrate the importance of addressing connected components, free variables, and caching. Experimental results indicate that our proposed approach for counting tree models of QBF formulas is highly efficient in practice, surpassing existing state-of-the-art methods designed for this specific purpose.

Modern solvers for quantified Boolean formulas (QBFs) process formulas in prenex form, which divides each QBF into two parts: the quantifier prefix and the propositional matrix. While this representation does not cover the full language of QBF, every non-prenex formula can be transformed to an equivalent formula in prenex form. This transformation offers several degrees of freedom and blurs structural information that might be useful for the solvers. In a case study conducted 20 years back, it has been shown that the applied transformation strategy heavily impacts solving time. We revisit this work and investigate how sensitive recent QBF solvers perform w.r.t. various prenexing strategies.

Recent approaches on verification and reasoning solve SAT and QBF encodings using state-of-the-art SMT solvers, as it “makes implementation much easier”. The ease-of-use of these solvers make SAT and QBF solvers less visible to users of solvers—who are maybe from different research communities—potentially not exploiting the power of state-of-the-art tools. In this work, we motivate the need to build bridges over the widening solver-gap and introduce Booleguru , a tool to convert between formats for logic formulas. It makes SAT and QBF solvers more accessible by using techniques known from SMT solvers, such as advanced Python interfaces like Z3Py and easily generatable languages like SMT-LIB, integrating them to our conversion tool. We then introduce a language to manipulate and combine multiple formulas, optionally applying transformations for quickly prototyping encodings. Booleguru ’s advanced scripting capabilities form a programming environment specialized for Boolean logic, offering a more efficient way to develop novel problem encodings.

Many problems for formal verification and artificial intelligence rely on advanced reasoning technologies in the background, often in the form of SAT or QBF solvers. Such solvers are sophisticated and highly tuned pieces of software, often too complex to be verified themselves. Now the question arises how one can one be sure that the result of such a solver is correct, especially when its result is critical for proving the correctness of another system. If a SAT solver, a tool for deciding a propositional formula, returns satisfiable, then it also returns a model which is easy to check. If the answer is unsatisfiable, the situation is more complicated. And so it is for true and false quantified Boolean formulas (QBFs), which extend propositional logic by quantifiers over the Boolean variables. To increase the trust in a solving result, modern solvers are expected to produce certificates that can independently and efficiently be checked. In this paper, we give an overview of the state of the art on validating the results of SAT and QBF solvers based on certification.KeywordsSATQBFCertification

As the application of quantified Boolean formulas (QBF) continues to expand in various scientific and industrial domains, the development of efficient QBF solvers and their underlying proving strategies is of growing importance. To understand and to compare different solving approaches, techniques of proof complexity are applied. To this end, formula families have been crafted that exhibit certain properties of proof systems. These formulas are valuable to test and compare specific solver implementations. Traditionally, the focus is on false formulas, in this work we extend the formula generator QBFFam to produce true formulas based on two popular formula families from proof complexity. KeywordsQBFSolverBenchmarkingKBKFQParity

Over the last years, innovative parallel and distributed SAT solving techniques were presented that could impressively exploit the power of modern hardware and cloud systems. Two approaches were particularly successful: (1) search-space splitting in a Divide-and-Conquer (D &C) manner and (2) portfolio-based solving. The latter executes different solvers or configurations of solvers in parallel. For quantified Boolean formulas (QBFs), the extension of propositional logic with quantifiers, there is surprisingly little recent work in this direction compared to SAT. In this paper, we present ParaQooba , a novel framework for parallel and distributed QBF solving which combines D &C parallelization and distribution with portfolio-based solving. Our framework is designed in such a way that it can be easily extended and arbitrary sequential QBF solvers can be integrated out of the box, without any programming effort. We show how ParaQooba orchestrates the collaboration of different solvers for joint problem solving by performing an extensive evaluation on benchmarks from QBFEval’22, the most recent QBF competition.