Quantum Programming Made Easy

We present IQu, namely a quantum programming language that extends Reynold's Idealized Algol, the paradigmatic core of Algol-like languages. IQu combines imperative programming with high-order features, mediated by a simple type theory. IQu mildly merges its quantum features with the classical programming style that we can experiment through Idealized Algol, the aim being to ease a transition towards the quantum programming world. The proposed extension is done along two main directions. First, IQu makes the access to quantum co-processors by means of quantum stores. Second, IQu includes some support for the direct manipulation of quantum circuits, in accordance with recent trends in the development of quantum programming languages. Finally, we show that IQu is quite effective in expressing well-known quantum algorithms.Comment: In Proceedings Linearity-TLLA 2018, arXiv:1904.0615

Diagnosis on a sliding window for partially observable Petri nets

summary:In this paper, we propose an algebraic approach to investigate the diagnosis of partially observable labeled Petri nets based on state estimation on a sliding window of a predefined length $h$. Given an observation, the resulting diagnosis state can be computed while solving integer linear programming problems with a reduced subset of basis markings. The proposed approach consists in exploiting a subset of $h$ observations at each estimation step, which provides a partial diagnosis relevant to the current observation window. This technique allows a status update with a "forgetfulness" of past observations and enables distinguishing repetitive and punctual faults. The complete diagnosis state can be defined as a function of the partial diagnosis states interpreted on the sliding window. As the analysis shows that some basis markings can present an inconsistency with a future evolution, which possibly implies unnecessary computations of basis markings, a withdrawal procedure of these irrelevant basis markings based on linear programming is proposed

A multiphase optimal control method for multi-train control and scheduling on railway lines

We consider a combined train control and scheduling problem involving multiple trains in a railway line with a predetermined departure/arrival sequence of the trains at stations and meeting points along the line. The problem is formulated as a multiphase optimal control problem while incorporating complex train running conditions (including undulating track, variable speed restrictions, running resistances, speed-dependent maximum tractive/braking forces) and practical train operation constraints on departure/arrival/running/dwell times. Two case studies are conducted. The first case illustrates the control and scheduling problem of two trains in a small artificial network with three nodes, where one train follows and overtakes the other. The second case optimizes the control and timetable of a single train in a subway line. The case studies demonstrate that the proposed framework can provide an effective approach in solving the combined train scheduling and control problem for reducing energy consumption in railway operations

Unboundedness Problems for Languages of Vector Addition Systems

A vector addition system (VAS) with an initial and a final marking and transition labels induces a language. In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision procedures for such languages. This is especially true for checking properties that state the existence of infinitely many words of a particular shape. Informally, we call these unboundedness properties. We present a simple set of axioms for predicates that can express unboundedness properties. Our main result is that such a predicate is decidable for VAS languages as soon as it is decidable for regular languages. Among other results, this allows us to show decidability of (i) separability by bounded regular languages, (ii) unboundedness of occurring factors from a language K with mild conditions on K, and (iii) universality of the set of factors

New Solution Methods for Joint Chance-Constrained Stochastic Programs with Random Left-Hand Sides

We consider joint chance-constrained programs with random lefthand sides. The motivation of this project is that this class of problem has many important applications, but there are few existing solution methods. For the most part, we deal with the subclass of problems for which the underlying parameter distributions are discrete. This assumption allows the original problem to be formulated as a deterministic equivalent mixed-integer program. We rst approach the problem as a mixed-integer program and derive a class of optimality cuts based on irreducibly infeasible subsets of the constraints of the scenarios of the problem. The IIS cuts can be computed effciently by means of a linear program. We give a method for improving the upper bound of the problem when no IIS cut can be identifi ed. We also give an implementation of an algorithm incorporating these ideas and finish with some computational results. We present a tabu search metaheuristic for fi nding good feasible solutions to the mixed-integer formulation of the problem. Our heuristic works by de ning a sufficient set of scenarios with the characteristic that all other scenarios do not have to be considered when generating upper bounds. We then use tabu search on the one-opt neighborhood of the problem. We give computational results that show our metaheuristic outperforming the state-of-the-art industrial solvers. We then show how to reformulate the problem so that the chance-constraints are monotonic functions. We then derive a convergent global branch-and-bound algorithm using the principles of monotonic optimization. We give a finitely convergent modi cation of the algorithm. Finally, we give a discussion on why this algorithm is computationally ine ffective. The last section of this dissertation details an application of joint chance-constrained stochastic programs to a vaccination allocation problem. We show why it is necessary to formulate the problem with random parameters and also why chance-constraints are a good framework for de fining an optimal policy. We give an example of the problem formulated as a chance constraint and a short numerical example to illustrate the concepts

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Tools and Algorithms for the Construction and Analysis of Systems

This book is Open Access under a CC BY licence. The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019. The total of 42 full and 8 short tool demo papers presented in these volumes was carefully reviewed and selected from 164 submissions. The papers are organized in topical sections as follows: Part I: SAT and SMT, SAT solving and theorem proving; verification and analysis; model checking; tool demo; and machine learning. Part II: concurrent and distributed systems; monitoring and runtime verification; hybrid and stochastic systems; synthesis; symbolic verification; and safety and fault-tolerant systems

Discrete Riemannian Calculus and A Posteriori Error Control on Shape Spaces

In this thesis, a novel discrete approximation of the curvature tensor on Riemannian manifolds is derived, efficient methods to interpolate and extrapolate images in the context of the time discrete metamorphosis model are analyzed, and an a posteriori error estimator for the binary Mumford–Shah model is examined. Departing from the variational time discretization on (possibly infinite-dimensional) Riemannian manifolds originally proposed by Rumpf and Wirth, in which a consistent time discrete approximation of geodesic curves, the logarithm, the exponential map and parallel transport is analyzed, we construct the discrete curvature tensor and prove its convergence under certain smoothness assumptions. To this end, several time discrete parallel transports are applied to suitably rescaled tangent vectors, where each parallel transport is computed using Schild’s ladder. The associated convergence proof essentially relies on multiple Taylor expansions incorporating symmetry and scaling relations. In several numerical examples we validate this approach for surfaces. The by now classical flow of diffeomorphism approach allows the transport of image intensities along paths in time, which are characterized by diffeomorphisms, and the brightness of each image particle is assumed to be constant along each trajectory. As an extension, the metamorphosis model proposed by Trouvé, Younes and coworkers allows for intensity variations of the image particles along the paths, which is reflected by an additional penalization term appearing in the energy functional that quantifies the squared weak material derivative. Taking into account the aforementioned time discretization, we propose a time discrete metamorphosis model in which the associated time discrete path energy consists of the sum of squared L2-mismatch functionals of successive square-integrable image intensity functions and a regularization functional for pairwise deformations. Our main contributions are the existence proof of time discrete geodesic curves in the context of this model, which are defined as minimizers of the time discrete path energy, and the proof of the Mosco-convergence of a suitable interpolation of the time discrete to the time continuous path energy with respect to the L2-topology. Using an alternating update scheme as well as a multilinear finite element respectively cubic spline discretization for the images and deformations allows to efficiently compute time discrete geodesic curves. In several numerical examples we demonstrate that time discrete geodesics can be robustly computed for gray-scale and color images. Taking into account the time discretization of the metamorphosis model we define the discrete exponential map in the space of images, which allows image extrapolation of arbitrary length for given weakly differentiable initial images and variations. To this end, starting from a suitable reformulation of the Euler–Lagrange equations characterizing the one-step extrapolation a fixed point iteration is employed to establish the existence of critical points of the Euler–Lagrange equations provided that the initial variation is small in L2. In combination with an implicit function type argument requiring H1-closeness of the initial variation one can prove the local existence as well as the local uniqueness of the discrete exponential map. The numerical algorithm for the one-step extrapolation is based on a slightly modified fixed point iteration using a spatial Galerkin scheme to obtain the optimal deformation associated with the unknown image, from which the unknown image itself can be recovered. To prove the applicability of the proposed method we compute the extrapolated image path for real image data. A common tool to segment images and shapes into multiple regions was developed by Mumford and Shah. The starting point to derive a posteriori error estimates for the binary Mumford–Shah model, which is obtained by restricting the original model to two regions, is a uniformly convex and non-constrained relaxation of the binary model following the work by Chambolle and Berkels. In particular, minimizers of the binary model can be exactly recovered from minimizers of the relaxed model via thresholding. Then, applying duality techniques proposed by Repin and Bartels allows deriving a consistent functional a posteriori error estimate for the relaxed model. Afterwards, an a posteriori error estimate for the original binary model can be computed incorporating a suitable cut-out argument in combination with the functional error estimate. To calculate minimizers of the relaxed model on an adaptive mesh described by a quadtree structure, we employ a primal-dual as well as a purely dual algorithm. The quality of the error estimator is analyzed for different gray-scale input images

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Process Mining Handbook

This is an open access book. This book comprises all the single courses given as part of the First Summer School on Process Mining, PMSS 2022, which was held in Aachen, Germany, during July 4-8, 2022. This volume contains 17 chapters organized into the following topical sections: Introduction; process discovery; conformance checking; data preprocessing; process enhancement and monitoring; assorted process mining topics; industrial perspective and applications; and closing