TY - CONF AB - A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating. AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A AU - Otop, Jan ID - 8600 SN - 18688969 T2 - 31st International Conference on Concurrency Theory TI - Multi-dimensional long-run average problems for vector addition systems with states VL - 171 ER - TY - CONF AB - A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both players have budgets, and in each turn, we hold an "auction" (bidding) to determine which player moves the token. In this survey, we consider several bidding mechanisms and study their effect on the properties of the game. Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly. We show how minor changes in the bidding mechanism lead to unexpected differences in the equivalence with random-turn games. AU - Avni, Guy AU - Henzinger, Thomas A ID - 8599 SN - 18688969 T2 - 31st International Conference on Concurrency Theory TI - A survey of bidding games on graphs VL - 171 ER - TY - CONF AB - The design and implementation of efficient concurrent data structures have seen significant attention. However, most of this work has focused on concurrent data structures providing good \emph{worst-case} guarantees. In real workloads, objects are often accessed at different rates, since access distributions may be non-uniform. Efficient distribution-adaptive data structures are known in the sequential case, e.g. the splay-trees; however, they often are hard to translate efficiently in the concurrent case. In this paper, we investigate distribution-adaptive concurrent data structures and propose a new design called the splay-list. At a high level, the splay-list is similar to a standard skip-list, with the key distinction that the height of each element adapts dynamically to its access rate: popular elements ``move up,'' whereas rarely-accessed elements decrease in height. We show that the splay-list provides order-optimal amortized complexity bounds for a subset of operations while being amenable to efficient concurrent implementation. Experimental results show that the splay-list can leverage distribution-adaptivity to improve on the performance of classic concurrent designs, and can outperform the only previously-known distribution-adaptive design in certain settings. AU - Aksenov, Vitaly AU - Alistarh, Dan-Adrian AU - Drozdova, Alexandra AU - Mohtashami, Amirkeivan ID - 8725 SN - 1868-8969 T2 - 34th International Symposium on Distributed Computing TI - The splay-list: A distribution-adaptive concurrent skip-list VL - 179 ER - TY - JOUR AB - Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement has measurable consequences. Here, we capture the essential features of spin-orbital entanglement in complex quantum matter utilizing 1D spin-orbital model which accommodates SU(2)⊗SU(2) symmetric Kugel-Khomskii superexchange as well as the Ising on-site spin-orbit coupling. Building on the results obtained for full and effective models in the regime of strong spin-orbit coupling, we address the question whether the entanglement found on superexchange bonds always increases when the Ising spin-orbit coupling is added. We show that (i) quantum entanglement is amplified by strong spin-orbit coupling and, surprisingly, (ii) almost classical disentangled states are possible. We complete the latter case by analyzing how the entanglement existing for intermediate values of spin-orbit coupling can disappear for higher values of this coupling. AU - Gotfryd, Dorota AU - Paerschke, Ekaterina AU - Wohlfeld, Krzysztof AU - Oleś, Andrzej M. ID - 8726 IS - 3 JF - Condensed Matter SN - 2410-3896 TI - Evolution of spin-orbital entanglement with increasing ising spin-orbit coupling VL - 5 ER - TY - CONF AB - Machine learning and formal methods have complimentary benefits and drawbacks. In this work, we address the controller-design problem with a combination of techniques from both fields. The use of black-box neural networks in deep reinforcement learning (deep RL) poses a challenge for such a combination. Instead of reasoning formally about the output of deep RL, which we call the wizard, we extract from it a decision-tree based model, which we refer to as the magic book. Using the extracted model as an intermediary, we are able to handle problems that are infeasible for either deep RL or formal methods by themselves. First, we suggest, for the first time, a synthesis procedure that is based on a magic book. We synthesize a stand-alone correct-by-design controller that enjoys the favorable performance of RL. Second, we incorporate a magic book in a bounded model checking (BMC) procedure. BMC allows us to find numerous traces of the plant under the control of the wizard, which a user can use to increase the trustworthiness of the wizard and direct further training. AU - Alamdari, Par Alizadeh AU - Avni, Guy AU - Henzinger, Thomas A AU - Lukina, Anna ID - 9040 SN - 9783854480426 T2 - Proceedings of the 20th Conference on Formal Methods in Computer-Aided Design TI - Formal methods with a touch of magic ER - TY - JOUR AB - Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system. AU - Biswas, Ranita AU - Largeteau-Skapin, Gaëlle AU - Zrour, Rita AU - Andres, Eric ID - 9249 IS - 1 JF - Mathematical Morphology - Theory and Applications SN - 2353-3390 TI - Digital objects in rhombic dodecahedron grid VL - 4 ER - TY - CONF AB - We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m⟶∞ . AU - Pach, János AU - Tardos, Gábor AU - Tóth, Géza ID - 9299 SN - 0302-9743 T2 - 28th International Symposium on Graph Drawing and Network Visualization TI - Crossings between non-homotopic edges VL - 12590 ER - TY - CONF AB - Second-order information, in the form of Hessian- or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems. Recently, there has been significant interest in utilizing this information in the context of deep neural networks; however, relatively little is known about the quality of existing approximations in this context. Our work examines this question, identifies issues with existing approaches, and proposes a method called WoodFisher to compute a faithful and efficient estimate of the inverse Hessian. Our main application is to neural network compression, where we build on the classic Optimal Brain Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms popular state-of-the-art methods for oneshot pruning. Further, even when iterative, gradual pruning is allowed, our method results in a gain in test accuracy over the state-of-the-art approaches, for standard image classification datasets such as ImageNet ILSVRC. We examine how our method can be extended to take into account first-order information, as well as illustrate its ability to automatically set layer-wise pruning thresholds and perform compression in the limited-data regime. The code is available at the following link, https://github.com/IST-DASLab/WoodFisher. AU - Singh, Sidak Pal AU - Alistarh, Dan-Adrian ID - 9632 SN - 10495258 T2 - Advances in Neural Information Processing Systems TI - WoodFisher: Efficient second-order approximation for neural network compression VL - 33 ER - TY - JOUR AB - Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context. AU - Edelsbrunner, Herbert AU - Virk, Ziga AU - Wagner, Hubert ID - 9630 IS - 2 JF - Journal of Computational Geometry TI - Topological data analysis in information space VL - 11 ER - TY - CONF AB - The ability to leverage large-scale hardware parallelism has been one of the key enablers of the accelerated recent progress in machine learning. Consequently, there has been considerable effort invested into developing efficient parallel variants of classic machine learning algorithms. However, despite the wealth of knowledge on parallelization, some classic machine learning algorithms often prove hard to parallelize efficiently while maintaining convergence. In this paper, we focus on efficient parallel algorithms for the key machine learning task of inference on graphical models, in particular on the fundamental belief propagation algorithm. We address the challenge of efficiently parallelizing this classic paradigm by showing how to leverage scalable relaxed schedulers in this context. We present an extensive empirical study, showing that our approach outperforms previous parallel belief propagation implementations both in terms of scalability and in terms of wall-clock convergence time, on a range of practical applications. AU - Aksenov, Vitaly AU - Alistarh, Dan-Adrian AU - Korhonen, Janne ID - 9631 SN - 10495258 T2 - Advances in Neural Information Processing Systems TI - Scalable belief propagation via relaxed scheduling VL - 33 ER -