An Automata-Theoretic Approach to the Verification of Distributed Algorithms

We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader). Processes have unique identifiers (pids) from an infinite, totally ordered domain. An algorithm proceeds in synchronous rounds, each round allowing a process to perform a bounded sequence of actions such as send or receive a pid, store it in some register, and compare register contents wrt. the associated total order. An algorithm is supposed to be correct independently of the number of processes. To specify correctness properties, we introduce a logic that can reason about processes and pids. Referring to leader election, it may say that, at the end of an execution, each process stores the maximum pid in some dedicated register. Since the verification of distributed algorithms is undecidable, we propose an underapproximation technique, which bounds the number of rounds. This is an appealing approach, as the number of rounds needed by a distributed algorithm to conclude is often exponentially smaller than the number of processes. We provide an automata-theoretic solution, reducing model checking to emptiness for alternating two-way automata on words. Overall, we show that round-bounded verification of distributed algorithms over rings is PSPACE-complete.Comment: 26 pages, 6 figure

Modelling end-pumped solid state lasers

The operation dynamics of end-pumped solid-state lasers are investigated by means of a spatially resolved numerical rate-equation model and a time-dependent analytical thermal model. The rate-equation model allows the optimization of parameters such as the output coupler transmission and gain medium length, with the aim of improving the laser output performance. The time-dependent analytical thermal model is able to predict the temperature and the corresponding induced thermal stresses on the pump face of quasi-continuous wave (qcw) end-pumped laser rods. Both models are found to be in very good agreement with experimental results

OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201

High-power diode-bar-pumped Nd:YLF laser at 1.053-µm

Scaling diode-pumped solid-state lasers to multiwatt average power levels is an area which has attracted growing interest over recent years, stimulated by the wide commercial availability and relatively low cost of high-power cw diode-bar pump sources. Recent developments in this area have included; efficient, TEM00, end-pumped Nd:YVO4 and side-pumped Nd:YLF lasers at 1.064µm and 1.047µm respectively with cw powers in excess of 13W. So far, the scaling of diode-pumped solid-state lasers to >10W average power, whilst retaining high overall efficiency has generally been restricted to only the highest gain Nd transitions. Extension of efficient high average power operation to include other useful, but lower gain, transitions such as the 1.053µm transition in Nd:YLF, has been hindered by the inconvenient shape of the diode bar's output beam. The diode bar, with its highly elongated emitting region produces an output having M2 beam quality factors ~1 in the plane perpendicular to the array, but >1000 in the plane of the array. It is therefore difficult to focus to the small beam sizes required, particularly for low gain transitions in efficient end-pumped configurations

Stable high repetition rate single frequency Q-switched Nd:YAG ring laser

Reliable single-frequency operation of a diode-pumped, Q-switched, Nd:YAG ring laser at high repetition frequencies up to 25kHz has been achieved by active stabilisation of the prelase power. Average powers of 250mW have been obtained for a 1.2 watt diode pump

Weighted Automata and Logics for Infinite Nested Words

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending B\"uchi's theorem to nested words. Recently, average and discounted computations of weights in quantitative systems found much interest. Here, we will introduce and investigate weighted automata models and weighted MSO logics for infinite nested words. As weight structures we consider valuation monoids which incorporate average and discounted computations of weights as well as the classical semirings. We show that under suitable assumptions, two resp. three fragments of our weighted logics can be transformed into each other. Moreover, we show that the logic fragments have the same expressive power as weighted nested word automata.Comment: LATA 2014, 12 page