Space Efficiency of Propositional Knowledge Representation Formalisms

We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class

Towards a Conceptual Framework Supporting Model Compilability

The ever-growing use of modeling languages today is largely due to a maturation of model-based development technologies. However, there is enough room for improving language specifications and consequently, the efficiency of their usage. The state of facts in specifying Well Formedness Rules is among the most important issues calling for improvements. Despite the fact that various papers have approached it, the topic is still open. To solve it, there is the need of a rigorous conceptual framework supporting the specification of modeling languages’ static semantics. This would stand as a basis for ensuring model compilability, a mandatory requirement in a model-driven context. Through this paper, we aim at providing core ideas that would contribute to the creation of such a framework. Our approach is testing-oriented and promotes the use of OCL specification patterns

Quantum utility -- definition and assessment of a practical quantum advantage

Several benchmarks have been proposed to holistically measure quantum computing performance. While some have focused on the end user's perspective (e.g., in application-oriented benchmarks), the real industrial value taking into account the physical footprint of the quantum processor are not discussed. Different use-cases come with different requirements for size, weight, power consumption, or data privacy while demanding to surpass certain thresholds of fidelity, speed, problem size, or precision. This paper aims to incorporate these characteristics into a concept coined quantum utility, which demonstrates the effectiveness and practicality of quantum computers for various applications where quantum advantage -- defined as either being faster, more accurate, or demanding less energy -- is achieved over a classical machine of similar size, weight, and cost. To successively pursue quantum utility, a level-based classification scheme -- constituted as application readiness levels (ARLs) -- as well as extended classification labels are introduced. These are demonstratively applied to different quantum applications from the fields of quantum chemistry, quantum simulation, quantum machine learning, and data analysis followed by a brief discussion

On the complexity of modified instances

Diese Dissertation untersucht die Komplexität modifizierter Instanzen und inwiefern sich NP-vollständige Probleme unter minimaler Veränderung stabil verhalten. Wir betrachten für verschiedene NP-vollständige Probleme, ob die Kenntnis einer Lösung einer Instanz eine Hilfe beim Entscheiden einer geringfügig modifizierten Instanz liefern kann. Außerdem untersuchen wir, inwieweit sich modifizierte Instanzen effizient entscheiden lassen, wenn nicht nur eine Lösung der unmodifizierten Instanz gegeben ist, sondern allgemeinere Hinweise, wie z.B. ein polynomiell langer String. Diese Fragestellung spielt nicht nur überall dort eine große Rolle, wo NP-vollständige Probleme in dynamischen Situationen schnell gelöst werden müssen, sondern liefert auch tiefere Einsichten in die generelle Natur der Klasse der NP-vollständigen Probleme. Des Weiteren betrachten wir das Problem der Reoptimierung. Das heißt, wir untersuchen für verschiedene Optimierungsprobleme, ob man für modifizierte Instanzen eines Optimierungsproblems eine gute Lösung finden kann, wenn bereits eine optimale Lösung einer ähnlichen Instanz bekannt ist