2,253 research outputs found

    A Parity Game Tale of Two Counters

    Get PDF
    Parity games are simple infinite games played on finite graphs with a winning condition that is expressive enough to capture nested least and greatest fixpoints. Through their tight relationship to the modal mu-calculus, they are used in practice for the model-checking and synthesis problems of the mu-calculus and related temporal logics like LTL and CTL. Solving parity games is a compelling complexity theoretic problem, as the problem lies in the intersection of UP and co-UP and is believed to admit a polynomial-time solution, motivating researchers to either find such a solution or to find superpolynomial lower bounds for existing algorithms to improve the understanding of parity games. We present a parameterized parity game called the Two Counters game, which provides an exponential lower bound for a wide range of attractor-based parity game solving algorithms. We are the first to provide an exponential lower bound to priority promotion with the delayed promotion policy, and the first to provide such a lower bound to tangle learning.Comment: In Proceedings GandALF 2019, arXiv:1909.0597

    Simple Fixpoint Iteration To Solve Parity Games

    Get PDF
    A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the many algorithms for parity games. We now consider a method of solving parity games by means of a naive fixpoint iteration. Several fixpoint algorithms for parity games have been proposed in the literature. In this work, we introduce an algorithm that relies on the notion of a distraction. The idea is that this offers a novel perspective for understanding parity games. We then show that this algorithm is in fact identical to two earlier published fixpoint algorithms for parity games and thus that these earlier algorithms are the same. Furthermore, we modify our algorithm to only partially recompute deeper fixpoints after updating a higher set and show that this modification enables a simple method to obtain winning strategies. We show that the resulting algorithm is simple to implement and offers good performance on practical parity games. We empirically demonstrate this using games derived from model-checking, equivalence checking and reactive synthesis and show that our fixpoint algorithm is the fastest solution for model-checking games.Comment: In Proceedings GandALF 2019, arXiv:1909.0597

    From Quasi-Dominions to Progress Measures

    Get PDF
    We revisit the approaches to the solution of parity games based on progress measures and show how the notion of quasi dominions can be integrated with those approaches. The idea is that, while progress measure based techniques typically focus on one of the two players, little information is gathered on the other player during the solution process. Adding quasi dominions provides additional information on this player that can be leveraged to greatly accelerate convergence to a progress measure. To accommodate quasi dominions, however, non trivial refinements of the approach are necessary. In particular, we need to introduce a novel notion of measure and a new method to prove correctness of the resulting solution technique

    Spartan Daily, February 21, 1935

    Get PDF
    Volume 23, Issue 89https://scholarworks.sjsu.edu/spartandaily/2267/thumbnail.jp

    The Worst-Case Complexity of Symmetric Strategy Improvement

    Full text link
    Symmetric strategy improvement is an algorithm introduced by Schewe et al. (ICALP 2015) that can be used to solve two-player games on directed graphs such as parity games and mean payoff games. In contrast to the usual well-known strategy improvement algorithm, it iterates over strategies of both players simultaneously. The symmetric version solves the known worst-case examples for strategy improvement quickly, however its worst-case complexity remained open. We present a class of worst-case examples for symmetric strategy improvement on which this symmetric version also takes exponentially many steps. Remarkably, our examples exhibit this behaviour for any choice of improvement rule, which is in contrast to classical strategy improvement where hard instances are usually hand-crafted for a specific improvement rule. We present a generalized version of symmetric strategy iteration depending less rigidly on the interplay of the strategies of both players. However, it turns out it has the same shortcomings

    A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games

    Get PDF
    The classic McNaughton-Zielonka algorithm for solving parity games has excellent performance in practice, but its worst-case asymptotic complexity is worse than that of the state-of-the-art algorithms. This work pinpoints the mechanism that is responsible for this relative underperformance and proposes a new technique that eliminates it. The culprit is the wasteful manner in which the results obtained from recursive calls are indiscriminately discarded by the algorithm whenever subgames on which the algorithm is run change. Our new technique is based on firstly enhancing the algorithm to compute attractor decompositions of subgames instead of just winning strategies on them, and then on making it carefully use attractor decompositions computed in prior recursive calls to reduce the size of subgames on which further recursive calls are made. We illustrate the new technique on the classic example of the recursive McNaughton-Zielonka algorithm, but it can be applied to other symmetric attractor-based algorithms that were inspired by it, such as the quasi-polynomial versions of the McNaughton-Zielonka algorithm based on universal trees

    Market Integration in the Golden Periphery - the Lisbon/London Exchange, 1854-1891

    Get PDF
    The existence of a self-regulating arbitrage mechanism under the gold standard has been traditionally considered as one of its main advantages, and attracted a corresponding research interest. This research is arguably relevant not only to test for the efficiency of the “gold points”, but also to study the evolution of financial integration during the so-called first era of globalization. Our first aim with this paper is to contribute to the enlargement of the scope of the literature by considering the case of Portugal that adhered to the system, in 1854, at a much earlier phase than the majority of countries, thus allowing for a broader perspective on the evolution of the efficiency of the foreign exchange market. As a typical “peripheral” country, Portugal can be used as the starting point for a study of the degree of integration of the periphery within the system. Furthermore, the Portuguese exchange also illustrates the role in practice of large players in sustaining currency stability, over and beyond the atomistic forces of arbitrage and speculation assumed in conventional theoretical frameworks. We also address the question of the credibility of the authorities’ commitment to the standard, through the perspective of the target zone literature.

    Modern Philippine Poetry in the Formative Years: 1920-1950

    Get PDF
    Excerpt Modern Philippine poetry in English originated in the 1920\u27s and began to come of age in the 1930\u27s. Although at the outset the poetry was overly sentimental and imitative, by the mid-1930\u27s several poets had developed their art to a promising degree. Then advancement of Philippine poetry was halted by the Japanese occupation of World Wa r II and by chaotic conditions in the first few post-war years. It was not until the 1950\u27s, therefore, that the poetry finally matured. This curve of development in Philippine letters can be traced in the early works of three of the greatest Philippine writers of the modern period : Bienvenido N . Santos, N . V . M . Gonzalez, and Carlos Bulosan
    corecore