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Boolean Satisfiability (SAT) is one of the problems at the core of theoretical computer science. It was the first problem proven to be NP-complete by Cook and, independently, by Levin. Nowadays it is conjectured that SAT cannot be solved in sub-exponential time. Thus, it is generally assumed that SAT and its restricted version k-SAT are hard to solve. However, state-of-the-art SAT solvers can solve even huge practical instances of these problems in a reasonable amount of time.
Why is SAT hard in theory, but easy in practice? One approach to answering this question is investigating the average runtime of SAT. In order to analyze this average runtime the random k-SAT model was introduced. The model generates all k-SAT instances with n variables and m clauses with uniform probability. Researching random k-SAT led to a multitude of insights and tools for analyzing random structures in general. One major observation was the emergence of the so-called satisfiability threshold: A phase transition point in the number of clauses at which the generated formulas go from asymptotically almost surely satisfiable to asymptotically almost surely unsatisfiable. Additionally, instances around the threshold seem to be particularly hard to solve.
In this thesis we analyze a more general model of random k-SAT that we call non-uniform random k-SAT. In contrast to the classical model each of the n Boolean variables now has a distinct probability of being drawn. For each of the m clauses we draw k variables according to the variable distribution and choose their signs uniformly at random. Non-uniform random k-SAT gives us more control over the distribution of Boolean variables in the resulting formulas. This allows us to tailor distributions to the ones observed in practice. Notably, non-uniform random k-SAT contains the previously proposed models random k-SAT, power-law random k-SAT and geometric random k-SAT as special cases.
We analyze the satisfiability threshold in non-uniform random k-SAT depending on the variable probability distribution. Our goal is to derive conditions on this distribution under which an equivalent of the satisfiability threshold conjecture holds. We start with the arguably simpler case of non-uniform random 2-SAT. For this model we show under which conditions a threshold exists, if it is sharp or coarse, and what the leading constant of the threshold function is. These are exactly the three ingredients one needs in order to prove or disprove the satisfiability threshold conjecture. For non-uniform random k-SAT with k=3 we only prove sufficient conditions under which a threshold exists. We also show some properties of the variable probabilities under which the threshold is sharp in this case. These are the first results on the threshold behavior of non-uniform random k-SAT.
The “HPI Future SOC Lab” is a cooperation of the Hasso Plattner Institute (HPI) and industry partners. Its mission is to enable and promote exchange and interaction between the research community and the industry partners.
The HPI Future SOC Lab provides researchers with free of charge access to a complete infrastructure of state of the art hard and software. This infrastructure includes components, which might be too expensive for an ordinary research environment, such as servers with up to 64 cores and 2 TB main memory. The offerings address researchers particularly from but not limited to the areas of computer science and business information systems. Main areas of research include cloud computing, parallelization, and In-Memory technologies.
This technical report presents results of research projects executed in 2017. Selected projects have presented their results on April 25th and November 15th 2017 at the Future SOC Lab Day events.
Technical report
(2019)
Design and Implementation of service-oriented architectures imposes a huge number of research questions from the fields of software engineering, system analysis and modeling, adaptability, and application integration. Component orientation and web services are two approaches for design and realization of complex web-based system. Both approaches allow for dynamic application adaptation as well as integration of enterprise application.
Commonly used technologies, such as J2EE and .NET, form de facto standards for the realization of complex distributed systems. Evolution of component systems has lead to web services and service-based architectures. This has been manifested in a multitude of industry standards and initiatives such as XML, WSDL UDDI, SOAP, etc. All these achievements lead to a new and promising paradigm in IT systems engineering which proposes to design complex software solutions as collaboration of contractually defined software services.
Service-Oriented Systems Engineering represents a symbiosis of best practices in object-orientation, component-based development, distributed computing, and business process management. It provides integration of business and IT concerns.
The annual Ph.D. Retreat of the Research School provides each member the opportunity to present his/her current state of their research and to give an outline of a prospective Ph.D. thesis. Due to the interdisciplinary structure of the research school, this technical report covers a wide range of topics. These include but are not limited to: Human Computer Interaction and Computer Vision as Service; Service-oriented Geovisualization Systems; Algorithm Engineering for Service-oriented Systems; Modeling and Verification of Self-adaptive Service-oriented Systems; Tools and Methods for Software Engineering in Service-oriented Systems; Security Engineering of Service-based IT Systems; Service-oriented Information Systems; Evolutionary Transition of Enterprise Applications to Service Orientation; Operating System Abstractions for Service-oriented Computing; and Services Specification, Composition, and Enactment.