Local Strategy Improvement for Parity Game Solving

The problem of solving a parity game is at the core of many problems in model checking, satisfiability checking and program synthesis. Some of the best algorithms for solving parity game are strategy improvement algorithms. These are global in nature since they require the entire parity game to be present at the beginning. This is a distinct disadvantage because in many applications one only needs to know which winning region a particular node belongs to, and a witnessing winning strategy may cover only a fractional part of the entire game graph. We present a local strategy improvement algorithm which explores the game graph on-the-fly whilst performing the improvement steps. We also compare it empirically with existing global strategy improvement algorithms and the currently only other local algorithm for solving parity games. It turns out that local strategy improvement can outperform these others by several orders of magnitude

Multidimensional perfect fluid cosmology with stable compactified internal dimensions

Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is achieved for a special class of perfect fluids. The external space behaves in accordance with the standard Friedmann model. Necessary restrictions on the parameters of the models are found to ensure dynamical behavior of the external (our) universe in agreement with observations.Comment: 11 pages, Latex2e, uses IOP packages, submitted to Class.Quant.Gra

Combinatorial simplex algorithms can solve mean payoff games

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff games. Moreover, any combinatorial simplex algorithm with a strongly polynomial complexity (the existence of such an algorithm is open) would provide in this way a strongly polynomial algorithm solving mean payoff games. Mean payoff games are known to be in NP and co-NP; whether they can be solved in polynomial time is an open problem. Our algorithm relies on a tropical implementation of the simplex method over a real closed field of Hahn series. One of the key ingredients is a new scheme for symbolic perturbation which allows us to lift an arbitrary mean payoff game instance into a non-degenerate linear program over Hahn series.Comment: v1: 15 pages, 3 figures; v2: improved presentation, introduction expanded, 18 pages, 3 figure

Stress variations near surfaces in diamond-like amorphous carbon

Using Monte Carlo simulations within the empirical potential approach, we examine the effect produced by the surface environment on the atomic level stresses in tetrahedral amorphous carbon. Both the distribution of stresses and the distributions of sp^2 and sp^3 atoms as a function of depth from the surface are highly inhomogeneous. They show the same close relationship between local stress and bonding hybridization found previously in the bulk of the material. Compressive local stress favors the formation of sp^3 sites, while tensile stress favors the formation of sp^2 sites.Comment: 7pages, 4 figure

Symmetric Strategy Improvement

Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We develop a novel symmetric strategy improvement algorithm where, in each iteration, the strategies of both players are improved simultaneously. We show that symmetric strategy improvement defies Friedmann's traps, which shook the belief in the potential of classic strategy improvement to be polynomial

Professional or amateur? The phonological output buffer as a working memory operator

The Phonological Output Buffer (POB) is thought to be the stage in language production where phonemes are held in working memory and assembled into words. The neural implementation of the POB remains unclear despite a wealth of phenomenological data. Individuals with POB impairment make phonological errors when they produce words and non-words, including phoneme omissions, insertions, transpositions, substitutions and perseverations. Errors can apply to different kinds and sizes of units, such as phonemes, number words, morphological affixes, and function words, and evidence from POB impairments suggests that units tend to substituted with units of the same kind-e.g., numbers with numbers and whole morphological affixes with other affixes. This suggests that different units are processed and stored in the POB in the same stage, but perhaps separately in different mini-stores. Further, similar impairments can affect the buffer used to produce Sign Language, which raises the question of whether it is instantiated in a distinct device with the same design. However, what appear as separate buffers may be distinct regions in the activity space of a single extended POB network, connected with a lexicon network. The self-consistency of this idea can be assessed by studying an autoassociative Potts network, as a model of memory storage distributed over several cortical areas, and testing whether the network can represent both units of word and signs, reflecting the types and patterns of errors made by individuals with POB impairment

Explaining the Electroweak Scale and Stabilizing Moduli in M Theory

In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua without fluxes, all moduli are stabilized by the effective potential and a stable hierarchy is generated, consistent with standard gauge unification. This paper explains the results of \cite{Acharya:2006ia} in more detail and generalizes them, finding an essentially unique de Sitter (dS) vacuum under reasonable conditions. One of the main phenomenological consequences is a prediction which emerges from this entire class of vacua: namely gaugino masses are significantly suppressed relative to the gravitino mass. We also present evidence that, for those vacua in which the vacuum energy is small, the gravitino mass, which sets all the superpartner masses, is automatically in the TeV - 100 TeV range.Comment: 73 pages, 39 figures, Minor typos corrected, Figures and References adde