Mikoláš Janota

Reasoning about Feature Models in Higher-Order Logic

A mechanically formalized feature modeling meta-model is presented. This theory is a generic higher-order formalization of a mathematical model synthesizing several feature modeling approaches found in the literature. This meta-model supports not only a better understanding of the various approaches to feature modeling, but also supports reasoning about and within feature model approaches, feature models, and on feature trees and their configurations.

Minimal sets over monotone predicates in boolean formulae

The importance and impact of the Boolean satisfiability (SAT) problem in many practical settings is well-known. Besides SAT, a number of computational problems related with Boolean formulas find a wide range of practical applications. Concrete examples for CNF formulas include computing prime implicates (PIs), minimal models (MMs), minimal unsatisfiable subsets (MUSes), minimal equivalent subsets (MESes) and minimal correction subsets (MCSes), among several others. This paper builds on earlier work by Bradley and Manna and shows that all these computational problems can be viewed as computing a minimal set subject to a monotone predicate, i.e. the MSMP problem. Thus, if cast as instances of the MSMP problem, these computational problems can be solved with the same algorithms. More importantly, the insights provided by this result allow developing a new algorithm for the general MSMP problem, that is asymptotically optimal. Moreover, in contrast with other asymptotically optimal algorithms, the new algorithm performs competitively in practice. The paper carries out a comprehensive experimental evaluation of the new algorithm on the MUS problem, and demonstrates that it outperforms state of the art MUS extraction algorithms.

Abstraction-based algorithm for 2QBF

Quantified Boolean Formulas (QBFs) enable standard representation of PSPACE problems. In particular, formulas with two quantifier levels (2QBFs) enable representing problems in the second level of the polynomial hierarchy (Π2P, Σ;2P). This paper proposes an algorithm for solving 2QBF satisfiability by counterexample guided abstraction refinement (CEGAR). This represents an alternative approach to 2QBF satisfiability and, by extension, to solving decision problems in the second level of polynomial hierarchy. In addition, the paper presents a comparison of a prototype implementing the presented algorithm to state of the art QBF solvers, showing that a larger set of instances is solved.

Formal approach to integrating feature and architecture models

If we model a family of software applications with a feature model and an architecture model, we are describing the same subject from different perspectives. Hence, we are running the risk of inconsistencies. For instance, the feature model might allow feature configurations that are not realizable by the architecture. In this paper we tackle this problem by providing a formalization of dependencies between features and components. Further, we demonstrate that this formalization offers a better understanding of the modeled concepts. Moreover, we propose automated techniques that derive additional information and provide feedback to the user. Finally, we discuss how some of these techniques can be implemented.

Proof complexity of resolution-based QBF calculi

Proof systems for quantified Boolean formulas (QBFs) provide a theoretical underpinning for the performance of important QBF solvers. However, the proof complexity of these proof systems is currently not well understood and in particular lower bound techniques are missing. In this paper we exhibit a new and elegant proof technique for showing lower bounds in QBF proof systems based on strategy extraction. This technique provides a direct transfer of circuit lower bounds to lengths of proofs lower bounds. We use our method to show the hardness of a natural class of parity formulas for Q-resolution and universal Q-resolution. Variants of the formulas are hard for even stronger systems as long-distance Q-resolution and extensions. With a completely different lower bound argument we show the hardness of the prominent formulas of Kleine Buning et al. [34] for the strong expansion-based calculus IR-calc. Our lower bounds imply new exponential separations between two different types of resolution-based QBF calculi: proof systems for CDCL-based solvers (Q-resolution, long-distance Q-resolution) and proof systems for expansion-based solvers (forallExp+Res and its generalizations IR-calc and IRM-calc). The relations between proof systems from the two different classes were not known before.

Model Construction with External Constraints: An Interactive Journey from Semantics to Syntax

Mainstream development environments have recently assimilated guidance technologies based on constraint satisfaction. We investigate one class of such technologies, namely, interactive guided derivation of models, where the editing system assists a designer by providing hints about valid editing operations that maintain global correctness. We provide a semantics-based classification of such guidance systems and investigate concrete guidance algorithms for two kinds of modeling languages: a simple subset of class-diagram-like language and for feature models. Both algorithms are efficient and provide exhaustive guidance.

Expansion-based QBF solving versus Q-resolution

This article introduces and studies a proof system ?Exp+Res that enables us to refute quantified Boolean formulas (QBFs). The system ?Exp+Res operates in two stages: it expands all universal variables through conjunctions and refutes the result by propositional resolution. This approach contrasts with the Q-resolution calculus, which enables refuting QBFs by rules similar to propositional resolution. In practice, Q-resolution enables producing proofs from conflict-driven DPLL-based QBF solvers. The system ?Exp+Res can on the other hand certify certain expansion-based solvers. So a natural question is to ask which of the systems, Q-resolution and ?Exp+Res, is more powerful? The article gives several partial responses to this question. On the positive side, we show that ?Exp+Res can p-simulate tree Q-resolution. On the negative side, we show that ?Exp+Res does not p-simulate unrestricted Q-resolution. In the favor of ?Exp+Res we show that ?Exp+Res is more powerful than a certain fragment of Q-resolution, which is important for DPLL-based QBF solving.

On propositional QBF expansions and q-resolution

Over the years, proof systems for propositional satisfiability (SAT) have been extensively studied. Recently, proof systems for quantified Boolean formulas (QBFs) have also been gaining attention. Q-resolution is a calculus enabling producing proofs from DPLL-based QBF solvers. While DPLL has become a dominating technique for SAT, QBF has been tackled by other complementary and competitive approaches. One of these approaches is based on expanding variables until the formula contains only one type of quantifier; upon which a SAT solver is invoked. This approach motivates the theoretical analysis carried out in this paper. We focus on a two phase proof system, which expands the formula in the first phase and applies propositional resolution in the second. Fragments of this proof system are defined and compared to Q-resolution.

Solving QBF with counterexample guided refinement

Abstract This article puts forward the application of Counterexample Guided Abstraction Refinement (CEGAR) in solving the well-known PSPACE-complete problem of quantified Boolean formulas (QBF). The article studies the application of CEGAR in two scenarios. In the first scenario, CEGAR is used to expand quantifiers of the formula and subsequently a satisfiability (SAT) solver is applied. First it is shown how to do that for two levels of quantification and then it is generalized for arbitrary number of levels by recursion. It is also shown that these ideas can be generalized to non-prenex and non-CNF QBF solvers. In the second scenario, CEGAR is employed as an additional learning technique in an existing DPLL-based QBF solver. Experimental evaluation of the implemented prototypes shows that the CEGAR-driven solver outperforms existing solvers on a number of benchmark families and that the DPLL solver benefits from the additional type of learning.

Algorithms for computing backbones of propositional formulae

The problem of propositional satisfiability (SAT) has found a number of applications in both theoretical and practical computer science. In many applications, however, knowing a formulas satisfiability alone is insufficient. Often, some other properties of the formula need to be computed. This article focuses on one such property: the backbone of a formula, which is the set of literals that are true in all the formulas models. Backbones find theoretical applications in characterization of SAT problems and they also find practical applications in product configuration or fault localization. This article overviews existing algorithms for backbone computation and introduces two novel ones. Further, an extensive evaluation of the algorithms is presented. This evaluation demonstrates that one of the novel algorithms significantly outperforms the existing ones.