TY - JOUR AB - We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence. AU - Chalupa, Marek AU - Chatterjee, Krishnendu AU - Pavlogiannis, Andreas AU - Sinha, Nishant AU - Vaidya, Kapil ID - 10417 IS - POPL JF - Proceedings of the ACM on Programming Languages TI - Data-centric dynamic partial order reduction VL - 2 ER - TY - GEN AB - We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence. 1. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. 2. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our data-centric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewicz-based DPOR and our data-centric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes. AU - Chalupa, Marek AU - Chatterjee, Krishnendu AU - Pavlogiannis, Andreas AU - Sinha, Nishant AU - Vaidya, Kapil ID - 5456 SN - 2664-1690 TI - Data-centric dynamic partial order reduction ER - TY - CONF AB - Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider the classical birth-death Moran process where there are two types of individuals, namely, the residents with fitness 1 and mutants with fitness r. The fitness indicates the reproductive strength. The evolutionary dynamics happens as follows: in the initial step, in a population of all resident individuals a mutant is introduced, and then at each step, an individual is chosen proportional to the fitness of its type to reproduce, and the offspring replaces a neighbor uniformly at random. The process stops when all individuals are either residents or mutants. The probability that all individuals in the end are mutants is called the fixation probability, which is a key factor in the rate of evolution. We consider the problem of approximating the fixation probability. The class of algorithms that is extremely relevant for approximation of the fixation probabilities is the Monte-Carlo simulation of the process. Previous results present a polynomial-time Monte-Carlo algorithm for undirected graphs when r is given in unary. First, we present a simple modification: instead of simulating each step, we discard ineffective steps, where no node changes type (i.e., either residents replace residents, or mutants replace mutants). Using the above simple modification and our result that the number of effective steps is concentrated around the expected number of effective steps, we present faster polynomial-time Monte-Carlo algorithms for undirected graphs. Our algorithms are always at least a factor O(n2/ log n) faster as compared to the previous algorithms, where n is the number of nodes, and is polynomial even if r is given in binary. We also present lower bounds showing that the upper bound on the expected number of effective steps we present is asymptotically tight for undirected graphs. AU - Chatterjee, Krishnendu AU - Ibsen-Jensen, Rasmus AU - Nowak, Martin ID - 551 SN - 978-395977046-0 T2 - Leibniz International Proceedings in Informatics TI - Faster Monte Carlo algorithms for fixation probability of the Moran process on undirected graphs VL - 83 ER - TY - CONF AB - Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first player is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a meanpayoff condition). There are two variants of the problem, namely, the threshold problem where the quantitative goal is to ensure that the mean-payoff value is above a threshold, and the value problem where the quantitative goal is to ensure the optimal mean-payoff value; in both cases ensuring the qualitative parity objective. The previous best-known algorithms for game graphs with n vertices, m edges, parity objectives with d priorities, and maximal absolute reward value W for mean-payoff objectives, are as follows: O(nd+1 . m . w) for the threshold problem, and O(nd+2 · m · W) for the value problem. Our main contributions are faster algorithms, and the running times of our algorithms are as follows: O(nd-1 · m ·W) for the threshold problem, and O(nd · m · W · log(n · W)) for the value problem. For mean-payoff parity objectives with two priorities, our algorithms match the best-known bounds of the algorithms for mean-payoff games (without conjunction with parity objectives). Our results are relevant in synthesis of reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective). AU - Chatterjee, Krishnendu AU - Henzinger, Monika H AU - Svozil, Alexander ID - 552 SN - 978-395977046-0 T2 - Leibniz International Proceedings in Informatics TI - Faster algorithms for mean-payoff parity games VL - 83 ER - TY - CONF AB - We consider two player, zero-sum, finite-state concurrent reachability games, played for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. Player 1 wins iff a designated goal state is eventually visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed. Our main results are as follows: We show that: (i) the optimal bound on the patience of optimal and -optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. AU - Chatterjee, Krishnendu AU - Hansen, Kristofer AU - Ibsen-Jensen, Rasmus ID - 553 SN - 978-395977046-0 T2 - Leibniz International Proceedings in Informatics TI - Strategy complexity of concurrent safety games VL - 83 ER - TY - JOUR AB - In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500 (doi:10.4310/CMS.2016.v14. n6.a1)), it has been established that, for every arbitrarily slow convergence speed and every natural number d ? {4, 5, . . .}, there exist d-dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two (d = 2) and three (d = 3) space dimensions. AU - Gerencser, Mate AU - Jentzen, Arnulf AU - Salimova, Diyora ID - 560 IS - 2207 JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences SN - 13645021 TI - On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions VL - 473 ER - TY - BOOK AB - This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. AU - Erdös, László AU - Yau, Horng ID - 567 SN - 9-781-4704-3648-3 TI - A Dynamical Approach to Random Matrix Theory VL - 28 ER - TY - JOUR AB - We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z< r(f) := (g-1(0): ||g - f|| < r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z< r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r > 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C). AU - Franek, Peter AU - Krcál, Marek ID - 568 IS - 2 JF - Homology, Homotopy and Applications SN - 15320073 TI - Persistence of zero sets VL - 19 ER - TY - JOUR AB - Most phenotypes are determined by molecular systems composed of specifically interacting molecules. However, unlike for individual components, little is known about the distributions of mutational effects of molecular systems as a whole. We ask how the distribution of mutational effects of a transcriptional regulatory system differs from the distributions of its components, by first independently, and then simultaneously, mutating a transcription factor and the associated promoter it represses. We find that the system distribution exhibits increased phenotypic variation compared to individual component distributions - an effect arising from intermolecular epistasis between the transcription factor and its DNA-binding site. In large part, this epistasis can be qualitatively attributed to the structure of the transcriptional regulatory system and could therefore be a common feature in prokaryotes. Counter-intuitively, intermolecular epistasis can alleviate the constraints of individual components, thereby increasing phenotypic variation that selection could act on and facilitating adaptive evolution. AU - Lagator, Mato AU - Sarikas, Srdjan AU - Acar, Hande AU - Bollback, Jonathan P AU - Guet, Calin C ID - 570 JF - eLife SN - 2050084X TI - Regulatory network structure determines patterns of intermolecular epistasis VL - 6 ER - TY - JOUR AB - The actomyosin ring generates force to ingress the cytokinetic cleavage furrow in animal cells, yet its filament organization and the mechanism of contractility is not well understood. We quantified actin filament order in human cells using fluorescence polarization microscopy and found that cleavage furrow ingression initiates by contraction of an equatorial actin network with randomly oriented filaments. The network subsequently gradually reoriented actin filaments along the cell equator. This strictly depended on myosin II activity, suggesting local network reorganization by mechanical forces. Cortical laser microsurgery revealed that during cytokinesis progression, mechanical tension increased substantially along the direction of the cell equator, while the network contracted laterally along the pole-to-pole axis without a detectable increase in tension. Our data suggest that an asymmetric increase in cortical tension promotes filament reorientation along the cytokinetic cleavage furrow, which might have implications for diverse other biological processes involving actomyosin rings. AU - Spira, Felix AU - Cuylen Haering, Sara AU - Mehta, Shalin AU - Samwer, Matthias AU - Reversat, Anne AU - Verma, Amitabh AU - Oldenbourg, Rudolf AU - Sixt, Michael K AU - Gerlich, Daniel ID - 569 JF - eLife SN - 2050084X TI - Cytokinesis in vertebrate cells initiates by contraction of an equatorial actomyosin network composed of randomly oriented filaments VL - 6 ER -