Magdalena Widl

QBF Resolution Systems and Their Proof Complexities

Quantified Boolean formula (QBF) evaluation has a broad range of applications in computer science and is gaining increasing attention. Recent progress has shown that for a certain family of formulas, Q-resolution, which forms the foundation of learning in modern search-based QBF solvers, is exponentially inferior in proof size to two of its extensions: Q-resolution with resolution over universal literals (QU-resolution) and long-distance Q-resolution (LQ-resolution). The relative proof power between LQ-resolution and QU-resolution, however, remains unknown. In this paper, we show their incomparability by exponential separations on two families of QBFs, and further propose a combination of the two resolution methods to achieve an even more powerful proof system. These results may shed light on solver development with enhanced learning mechanisms. In addition, we show how QBF Skolem/Herbrand certificate extraction can benefit from polynomial LQ-resolution proofs in contrast to their exponential Q-resolution counterparts.

Long-Distance Resolution: Proof Generation and Strategy Extraction in Search-Based QBF Solving

Strategies (and certificates) for quantified Boolean formulas (QBFs) are of high practical relevance as they facilitate the verification of results returned by QBF solvers and the generation of solutions to problems formulated as QBFs. State of the art approaches to obtain strategies require traversing a Q-resolution proof of a QBF, which for many real-life instances is too large to handle. In this work, we consider the long-distance Q-resolution (LDQ) calculus, which allows particular tautological resolvents. We show that for a family of QBFs using the LDQ-resolution allows for exponentially shorter proofs compared to Q-resolution. We further show that an approach to strategy extraction originally presented for Q-resolution proofs can also be applied to LDQ-resolution proofs. As a practical application, we consider search-based QBF solvers which are able to learn tautological clauses based on resolution and the conflict-driven clause learning method. We prove that the resolution proofs produced by these solvers correspond to proofs in the LDQ calculus and can therefore be used as input for strategy extraction algorithms. Experimental results illustrate the potential of the LDQ calculus in search-based QBF solving.

Guided Merging of Sequence Diagrams

The employment of optimistic model versioning systems allows multiple developers of a team to work independently on their local copies of a software model. The merging process towards one consolidated version can be error-prone and time-consuming when performed without any tool support. Recently, several sophisticated approaches for model merging have been presented. However, even for multi-view modeling languages like UML, which distribute the information on the modeled system over different views, these views are merged independently of each other. Hence, inconsistencies are likely to be introduced into the merged model. We suggest to solve this problem by exploiting information stored in one view as constraint for the computation of a consolidated version of another view. More specifically, we demonstrate how state machines can guide the integration of parallel changes performed on a sequence diagram. We give a concise formal description of this problem and suggest a translation to the satisfiability problem of propositional logic.

Towards scenario-based testing of UML diagrams

In model-driven engineering, models are not primarily developed for documentation and requirement specification purposes, but promoted to first-class artifacts, from which executable code is generated. As a consequence, typical development activities like testing must be performed on the model level. In this paper, we propose to use overlapping information inherent in multiple views of models for automatic testing. Using a prototype based on the model checker Spin we show the feasibility of this approach and identify future challenges.

An improved memetic algorithm for break scheduling

In this paper we consider solving a complex real life break scheduling problem. This problem of high practical relevance arises in many working areas, e.g. in air traffic control and other fields where supervision personnel is working. The objective is to assign breaks to employees such that various constraints reflecting legal demands or ergonomic criteria are satisfied and staffing requirement violations are minimised. In our previous work we proposed a memetic algorithm for the assignment of breaks. We improve in this paper the previous method by proposing a new memetic representation, a new crossover and selection operator, and a penalty system that helps to select memes that have a better chance to be improved by a local search. Our approach is influenced by various parameters, for which we experimentally evaluate different settings. The impact of each parameter is statistically assessed. We compare our algorithm to state of the art results on a set of existing real life and randomly generated instances. Our new algorithm returns improved results on 28 out of the 30 benchmark instances. To the best of our knowledge, these results constitute current upper bounds for the respective instances.

The break scheduling problem: complexity results and practical algorithms

Break scheduling problems arise in working areas where breaks are indispensable, e.g., in air traffic control, supervision, or assembly lines. We regard such a problem from the area of supervision personnel. The objective is to find a break assignment for an existing shiftplan such that various constraints reflecting legal demands or ergonomic criteria are satisfied and such that staffing requirement violations are minimised. We prove the NP-completeness of this problem when all possible break patterns for each shift are given explicitly as part of the input. To solve our problem we propose two variations of a memetic algorithm. We define genetic operators, a local search based on three neighbourhoods, and a penalty system that helps to avoid local optima. Parameters influencing the algorithms are experimentally evaluated and assessed with statistical methods. We compare our algorithms, each with the best parameter setting according to the evaluation, with the state-of-the-art algorithm on a set of 30 real-life and randomly generated instances that are publicly available. One of our algorithms returns improved results on 28 out of the 30 benchmark instances. To the best of our knowledge, our improved results for the real-life instances constitute new upper bounds for this problem

A SAT-Based Debugging Tool for State Machines and Sequence Diagrams

An effective way to model message exchange in complex settings is to use UML sequence diagrams in combination with state machine diagrams. A natural question that arises in this context is whether these two views are consistent, i.e., whether a desired or forbidden scenario modeled in the sequence diagram can be or cannot be executed by the state machines.In case of an inconsistency, a concrete communication trace of the state machines can give valuable information for debugging purposes on the model level.This trace either hints to a message in the sequence diagram where the communication between the state machines fails, or describes a concrete forbidden communication trace between the state machines.To detect and explain such inconsistencies, we propose a novel SAT-based formalization which can be solved automatically by an off-the-shelf SAT solver. To this end, we present the formal and technical foundations needed for the SAT-encoding, and an implementation inside the Eclipse Modeling Framework (EMF). We evaluate the effectiveness of our approach using grammar-based fuzzing.

Test case generation by grammar-based fuzzing for model-driven engineering

Software models, traditionally used mainly for documentation and informal specification purposes, are becoming first-class development artifacts in the area of Modeldriven Engineering (MDE). In MDE, code is generated automatically from multi-view models described in languages like the Unified Modeling Language (UML). Maintaining consistency between the different views of a model is crucial for the generation of correct code.

Intra- and interdiagram consistency checking of behavioral multiview models

Multiview modeling languages like UML are a very powerful tool to deal with the ever increasing complexity of modern software systems. By splitting the description of a system into different views-the diagrams in the case of UML-system properties relevant for a certain development activity are highlighted while other properties are hidden. This multiview approach has many advantages for the human modeler, but at the same time it is very susceptible to various kinds of defects that may be introduced during the development process. Besides defects which relate only to one view, it can also happen that two different views, which are correct if considered independently, contain inconsistent information when combined. Such inconsistencies between different views usually indicate a defect in the model and can be critical if they propagate up to the executable system.In this paper, we present an approach to formally verify the reachability of a global state of a set of communicating UML state machines, i.e., we present a solution for an intradiagram consistency checking problem. We then extend this approach to solve an interdiagram consistency checking problem. In particular, we verify whether the message exchange modeled in a UML sequence diagram conforms to a set of communicating state machines.For solving both kinds of problems, we proceed as follows. As a first step, we formalize the semantics of UML state machines and of UML sequence diagrams. In the second step, we build upon this formal semantics and encode both verification tasks as decision problems of propositional logic (SAT) allowing the use of efficient SAT technology. We integrate both approaches in a graphical modeling environment, enabling modelers to use formal verification techniques without any special background knowledge. We experimentally evaluate the scalability of our approach. HighlightsFormalization of the semantics of a modeling language similar to UML.Consistency checking via SAT encodings.Direct integration of verification in modeling environment.