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This volume contains those research papers presented at the Second International Conference on Tests and Proofs (TAP 2008) that were not included in the main conference proceedings. TAP was the second conference devoted to the convergence of proofs and tests. It combines ideas from both areas for the advancement of software quality. To prove the correctness of a program is to demonstrate, through impeccable mathematical techniques, that it has no bugs; to test a program is to run it with the expectation of discovering bugs. On the surface, the two techniques seem contradictory: if you have proved your program, it is fruitless to comb it for bugs; and if you are testing it, that is surely a sign that you have given up on any hope of proving its correctness. Accordingly, proofs and tests have, since the onset of software engineering research, been pursued by distinct communities using rather different techniques and tools. And yet the development of both approaches leads to the discovery of common issues and to the realization that each may need the other. The emergence of model checking has been one of the first signs that contradiction may yield to complementarity, but in the past few years an increasing number of research efforts have encountered the need for combining proofs and tests, dropping earlier dogmatic views of their incompatibility and taking instead the best of what each of these software engineering domains has to offer. The first TAP conference (held at ETH Zurich in February 2007) was an attempt to provide a forum for the cross-fertilization of ideas and approaches from the testing and proving communities. For the 2008 edition we found the Monash University Prato Centre near Florence to be an ideal place providing a stimulating environment. We wish to sincerely thank all the authors who submitted their work for consideration. And we would like to thank the Program Committee members as well as additional referees for their great effort and professional work in the review and selection process. Their names are listed on the following pages. In addition to the contributed papers, the program included three excellent keynote talks. We are grateful to Michael Hennell (LDRA Ltd., Cheshire, UK), Orna Kupferman (Hebrew University, Israel), and Elaine Weyuker (AT&T Labs Inc., USA) for accepting the invitation to address the conference. Two very interesting tutorials were part of TAP 2008: "Parameterized Unit Testing with Pex" (J. de Halleux, N. Tillmann) and "Integrating Verification and Testing of Object-Oriented Software" (C. Engel, C. Gladisch, V. Klebanov, and P. Rümmer). We would like to express our thanks to the tutorial presenters for their contribution. It was a team effort that made the conference so successful. We are grateful to the Conference Chair and the Steering Committee members for their support. And we particularly thank Christoph Gladisch, Beate Körner, and Philipp Rümmer for their hard work and help in making the conference a success. In addition, we gratefully acknowledge the generous support of Microsoft Research Redmond, who financed an invited speaker.

Semantic descriptions of non-textual media available on the web can be used to facilitate retrieval and presentation of media assets and documents containing them. While technologies for multimedia semantic descriptions already exist, there is as yet no formal description of a high quality multimedia ontology that is compatible with existing (semantic) web technologies. We explain the complexity of the problem using an annotation scenario. We then derive a number of requirements for specifying a formal multimedia ontology, including: compatibility with MPEG-7, embedding in foundational ontologies, and modularisation including separation of document structure from domain knowledge. We then present the developed ontology and discuss it with respect to our requirements.

We aim to demonstrate that automated deduction techniques, in particular those following the model computation paradigm, are very well suited for database schema/query reasoning. Specifically, we present an approach to compute completed paths for database or XPath queries. The database schema and a query are transformed to disjunctive logic programs with default negation, using a description logic as an intermediate language. Our underlying deduction system, KRHyper, then detects if a query is satisfiable or not. In case of a satisfiable query, all completed paths -- those that fulfill all given constraints -- are returned as part of the computed models. The purpose of our approach is to dramatically reduce the workload on the query processor. Without the path completion, a usual XML query processor would search the database for solutions to the query. In the paper we describe the transformation in detail and explain how to extract the solution to the original task from the computed models. We understand this paper as a first step, that covers a basic schema/query reaÂsoning task by model-based deduction. Due to the underlying expressive logic formalism we expect our approach to easily adapt to more sophisticated problem settings, like type hierarchies as they evolve within the XML world.

Hyper tableaux with equality
(2007)

In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for paramodulation are drawn (only) from a set of positive unit clauses, the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many redundancy elimination techniques known from superposition theorem proving. Our main results are soundness and completeness, but we briefly describe the implementation, too.

The Living Book is a system for the management of personalized and scenario specific teaching material. The main goal of the system is to support the active, explorative and selfdetermined learning in lectures, tutorials and self study. The Living Book includes a course on 'logic for computer scientists' with a uniform access to various tools like theorem provers and an interactive tableau editor. It is routinely used within teaching undergraduate courses at our university. This paper describes the Living Book and the use of theorem proving technology as a core component in the knowledge management system (KMS) of the Living Book. The KMS provides a scenario management component where teachers may describe those parts of given documents that are relevant in order to achieve a certain learning goal. The task of the KMS is to assemble new documents from a database of elementary units called 'slices' (definitions, theorems, and so on) in a scenario-based way (like 'I want to prepare for an exam and need to learn about resolution'). The computation of such assemblies is carried out by a model-generating theorem prover for first-order logic with a default negation principle. Its input consists of meta data that describe the dependencies between different slices, and logic-programming style rules that describe the scenario-specific composition of slices. Additionally, a user model is taken into account that contains information about topics and slices that are known or unknown to a student. A model computed by the system for such input then directly specifies the document to be assembled. This paper introduces the elearning context we are faced with, motivates our choice of logic and presents the newly developed calculus used in the KMS.

The model evolution calculus
(2004)

The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proof procedure for first-order logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The recent FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the first-order level without resorting to ground instantiations. FDPLL lifts to the first-order case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful litfing of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, one of FDPLL's optimizations, and so has the potential of leading to much faster implementations.

E-KRHyper is a versatile theorem prover and model generator for firstorder logic that natively supports equality. Inequality of constants, however, has to be given by explicitly adding facts. As the amount of these facts grows quadratically in the number of these distinct constants, the knowledge base is blown up. This makes it harder for a human reader to focus on the actual problem, and impairs the reasoning process. We extend E-Hyper- underlying E-KRhyper tableau calculus to avoid this blow-up by implementing a native handling for inequality of constants. This is done by introducing the unique name assumption for a subset of the constants (the so called distinct object identifiers). The obtained calculus is shown to be sound and complete and is implemented into the E-KRHyper system. Synthetic benchmarks, situated in the theory of arrays, are used to back up the benefits of the new calculus.

Avoidance of routing loops
(2009)

We introduce a new routing algorithm which can detect routing loops by evaluating routing updates more thoroughly. Our new algorithm is called Routing with Metric based Topology Investigation (RMTI), which is based on the simple Routing Information Protocol (RIP) and is compatible to all RIP versions. In case of a link failure, a network can reorganize itself if there are redundant links available. Redundant links are only available in a network system like the internet if the topology contains loops. Therefore, it is necessary to recognize and to prevent routing loops. A routing loop can be seen as a circular trace of a routing update information which returns to the same router, either directly from the neighbor router or via a loop topology. Routing loops could consume a large amount of network bandwidth and could impact the endtoend performance of the network. Our RMTI approach is capable to improve the efficiency of Distance Vector Routing.

The University of Koblenz-Landau would like to apply for participation in the RoboCup Mixed Reality League in Suzhou, China 2008. Our team is composed of ten team members and two supervisors. All members are graduate students of Computational Visualistics. Our supervisors are Ph.D. candidates currently researching in the working groups of artificial intelligence and computer graphics.

Im Rahmen von Projekten haben die Mitarbeiter in einem Unternehmen oft komplexe Problemstellungen zu bearbeiten, für die es keine objektiv richtigen oder falschen Lösungen gibt. Stattdessen werden im Rahmen der Entwurfs- und Entscheidungsprozesse mehrere Lösungsvorschläge erarbeitet um dann unter Abwägung von Pro- und Contra-Argumenten eine möglichst optimale Lösung zu finden.