Nondeterministic functions and the existence of optimal proof systems

We provide new characterizations of two previously studied questions on nondeterministic function classes: Q1: Do nondeterministic functions admit efficient deterministic refinements? Q2: Do nondeterministic function classes contain complete functions? We show that Q1 for the class is equivalent to the question whether the standard proof system for SAT is p-optimal, and to the assumption that every optimal proof system is p-optimal. Assuming only the existence of a p-optimal proof system for SAT, we show that every set with an optimal proof system has a p-optimal proof system. Under the latter assumption, we also obtain a positive answer to Q2 for the class . An alternative view on nondeterministic functions is provided by disjoint sets and tuples. We pursue this approach for disjoint -pairs and its generalizations to tuples of sets from and with disjointness conditions of varying strength. In this way, we obtain new characterizations of Q2 for the class . Question Q1 for is equivalent to the question of whether every disjoint -pair is easy to separate. In addition, we characterize this problem by the question of whether every propositional proof system has the effective interpolation property. Again, these interpolation properties are intimately connected to disjoint -pairs, and we show how different interpolation properties can be modeled by -pairs associated with the underlying proof system

Middle East - North Africa and the millennium development goals : implications for German development cooperation

          Closed-loop controlled combustion is a promising technique to improve the overall performance of internal combustion engines and Diesel engines in particular. In order for this technique to be implemented some form of feedback from the combustion process is required. The feedback signal is processed and from it combustionrelated parameters are computed. These parameters are then fed to a control process which drives a series of outputs (e.g. injection timing in Diesel engines) to control their values. This paper’s focus lies on the processing and computation that is needed on the feedback signal before this is ready to be fed to the control process as well as on the electronics necessary to support it. A number of feedback alternatives are briefly discussed and for one of them, the in-cylinder pressure sensor, the CA50 (crank angle in which the integrated heat release curve reaches its 50% value) and the IMEP (Indicated Mean Effective Pressure) are identified as two potential control variables. The hardware architecture of a system capable of calculating both of them on-line is proposed and necessary feasibility size and speed considerations are made by implementing critical blocks in VHDL targeting a flash-based Actel ProASIC3 automotive-grade FPGA

Pattern matching in trace monoids

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Pattern Matching in Trace Monoids

An algorithm is presented solving the factor problem in trace monoids. Given two traces represented by words, the algorithm determines in linear time whether the first trace is a factor of the second one. The space used for this task is linear in the length of the first word. Similar to the Knuth-Morris-Pratt Algorithm for the factor problem on words, the algorithm simulates a finite automaton determined by the first word on the second word. To develop the algorithm, we examine overlaps of two traces, and show that they form a lattice. Finally we investigate the lattice of extensible trace pairs (which represent still extensible prefixes of a searched factor appearing in some other trace), because of their close relations to the structures used by the algorithm. 1 Introduction The pattern matching problem in free monoids is an extensively studied problem in computer science. For two words v; x 2 A it is asked whether there are words u; w 2 A such that x = uvw, i.e., it is..