Model-Checking the Higher-Dimensional Modal mu-Calculus

The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in polynomial time, and conversely every polynomial-time decidable problem that has a bisimulation-invariant encoding into labeled transition systems can also be defined in the higher-dimensional modal mu-calculus. We exemplify the latter connection by giving several examples of decision problems which reduce to model checking of the higher-dimensional modal mu-calculus for some fixed formulas. This way generic model checking algorithms for the logic can then be used via partial evaluation in order to obtain algorithms for theses problems which may benefit from improvements that are well-established in the field of program verification, namely on-the-fly and symbolic techniques. The aim of this work is to extend such techniques to other fields as well, here exemplarily done for process equivalences, automata theory, parsing, string problems, and games.Comment: In Proceedings FICS 2012, arXiv:1202.317

Buffered Simulation Games for B\"uchi Automata

Simulation relations are an important tool in automata theory because they provide efficiently computable approximations to language inclusion. In recent years, extensions of ordinary simulations have been studied, for instance multi-pebble and multi-letter simulations which yield better approximations and are still polynomial-time computable. In this paper we study the limitations of approximating language inclusion in this way: we introduce a natural extension of multi-letter simulations called buffered simulations. They are based on a simulation game in which the two players share a FIFO buffer of unbounded size. We consider two variants of these buffered games called continuous and look-ahead simulation which differ in how elements can be removed from the FIFO buffer. We show that look-ahead simulation, the simpler one, is already PSPACE-hard, i.e. computationally as hard as language inclusion itself. Continuous simulation is even EXPTIME-hard. We also provide matching upper bounds for solving these games with infinite state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527

Random homogenisation of a highly oscillatory singular potential

In this article, we consider the problem of homogenising the linear heat equation perturbed by a rapidly oscillating random potential. We consider the situation where the space-time scaling of the potential's oscillations is \textit{not} given by the diffusion scaling that leaves the heat equation invariant. Instead, we treat the case where spatial oscillations are much faster than temporal oscillations. Under suitable scaling of the amplitude of the potential, we prove convergence to a deterministic heat equation with constant potential, thus completing the results previously obtained in \cite{MR2962093}

Improved Modal Assurance Criterion using a quantification of identification errors per mode/sensor

Scanning laser vibrometer measurements generate detailed maps of modal characteristics in normal or 3D directions. Since many points are measured, individual validation of cannot be performed manually in a reasonable time frame and a notable fraction of measurements is expected to be fairly noisy. The key new notion of the paper is a quantification of identification error and level of contribution for each mode and each sensor based on the comparison of measured and synthesized transfers around each resonance. These criteria are shown to allow efficient analysis of the validity of large measurement sets to provide an automated procedure to select sensors that should be kept for each mode. This quantification, being performed before correlation, provides a priori estimates of sources of poor correlation associated with the identification process. It thus becomes possible to provide improved Modal Assurance Criterion estimations where, for each modeshape, sensors known to be incorrectly identified can be discarded. The 3D vibrometer scan of a brake component is used to illustrate the proposed strategies

Model-Checking Process Equivalences

Process equivalences are formal methods that relate programs and system which, informally, behave in the same way. Since there is no unique notion of what it means for two dynamic systems to display the same behaviour there are a multitude of formal process equivalences, ranging from bisimulation to trace equivalence, categorised in the linear-time branching-time spectrum. We present a logical framework based on an expressive modal fixpoint logic which is capable of defining many process equivalence relations: for each such equivalence there is a fixed formula which is satisfied by a pair of processes if and only if they are equivalent with respect to this relation. We explain how to do model checking, even symbolically, for a significant fragment of this logic that captures many process equivalences. This allows model checking technology to be used for process equivalence checking. We show how partial evaluation can be used to obtain decision procedures for process equivalences from the generic model checking scheme.Comment: In Proceedings GandALF 2012, arXiv:1210.202

An improved approach for automatic process plan generation of complex borings

The authors are grateful for funding provided to this project by the French Ministry of Industry, Dassault Aviation, Dassault Systemes, and F. Vernadat for his review and recommendations.The research concerns automated generation of process plans using knowledge formalization and capitalization. Tools allowing designers to deal with issues and specifications of the machining domain are taken into account. The main objective of the current work is to prevent designers from designing solutions that would be expensive and difficult to machine. Among all available solutions to achieve this goal, two are distinguished: the generative approach and the analogy approach. The generative approach is more adapted to generate the machining plans of parts composed of numerous boring operations in interaction. However, generative systems have two major problems: proposed solutions are often too numerous and are only geometrically but not technologically relevant. In order to overcome these drawbacks, two new concepts of feature and three control algorithms are developed. The paper presents the two new features: the Machining Enabled Geometrical Feature (MEGF) and the Machinable Features (MbF). This development is the result of the separation of the geometrical and the technological data contained in one machining feature. The second objective of the paper is to improve the current Process Ascending Generation (PAG) system with control algorithms in order to limit the combinatorial explosion and disable the generation of unusable or not machinable solutions

Exploiting technological synergies for future launch vehicles

Two launch vehicle concepts based on technologies available today or in a short term future in Western Europe are presented. The design of both launchers has the goal of exploiting synergies with current European programs to limit development and operational costs. Technologies of particular interest here are the high performance solid rocket motors with carbon-epoxy filament wound monolithic motor cases and the future high performance cryogenic expander cycle engine Vinci. The first concept dubbed ANGELA (A New GEneration LAuncher) is a study financed with funds of the German Ministry of Economics and managed by the DLR Space Administration. The project, which started in the summer of 2012 aims at designing a low cost versatile launcher able to place payloads between 2 and 5 tons into GTO. Three architectures have been considered during the first phase of the study. This phase was concluded in March 2013 with the preliminary stagings, which will be the starting point of more detailed analyses. The first architecture is made out of an H110 (stage with 110 tons of LOx/LH2) equipped with two Vulcain 2 engines with shortened nozzles and an H29 propelled by a Vinci engine. In addition the variation of the number of P36 solid rocket boosters allow to reach the entire range of payload performance. The second architecture differs from the first one only by the use of a new staged-combustion engine instead of two Vulcain 2 engines. The new engine, which should deliver 1800 kN in vacuum, allows a reduction of the size of the stages to H90-H24, enhanced with P34 boosters. The third and last architecture is a so called Multi PPH. The first stage is a bundle of 2 or 3 P120 solid rocket motors. The second stage is made out of one single P120, strictly similar to those used for the first stage. Finally the upper stage is an H23 equipped with a Vinci engine, the same as the two other architectures. The second launcher concept described in this paper is the small TSTO launch vehicle. It consists of a large solid rocket motor first stage P175 and a cryogenic upper stage propelled by the Vinci engine, H26. The preliminary design performed at DLR-SART considers two target performances. The light version of the small TSTO shall perform Galileo satellite replacement single launch missions to MTO corresponding to a payload performance of about 1400 kg in GTO. A heavy version of the launch vehicle shall be able to launch payloads up to 3000 kg in GTO. The performance increase for the heavy version is made possible by the addition of two pairs of P23 boosters, the second pair being ignited with a delay

The Tail-Recursive Fragment of Timed Recursive CTL

Timed Recursive CTL (TRCTL) was recently proposed as a merger of two extensions of the well-known branching-time logic CTL: Timed CTL on one hand is interpreted over real-time systems like timed automata, and Recursive CTL (RecCTL) on the other hand obtains high expressiveness through the introduction of a recursion operator. Model checking for the resulting logic is known to be 2-EXPTIME-complete. The aim of this paper is to investigate the possibility to obtain a fragment of lower complexity without losing too much expressive power. It is obtained by a syntactic property called "tail-recursiveness" that restricts the way that recursive formulas can be built. This restriction is known to decrease the complexity of model checking by half an exponential in the untimed setting. We show that this also works in the real-time world: model checking for the tail-recursive fragment of TRCTL is EXPSPACE-complete. The upper bound is obtained by a standard untiming construction via region graphs, and rests on the known complexity of tail-recursive fragments of higher-order modal logics. The lower bound is established by a reduction from a suitable tiling problem