2,253 research outputs found
A Parity Game Tale of Two Counters
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
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
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
Volume 23, Issue 89https://scholarworks.sjsu.edu/spartandaily/2267/thumbnail.jp
The Worst-Case Complexity of Symmetric Strategy Improvement
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
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
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
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
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