Fatal Attractors in Parity Games: Building Blocks for Partial Solvers

Attractors in parity games are a technical device for solving "alternating" reachability of given node sets. A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively. We here propose new forms of attractors that are monotone in that they are aware of specific static patterns of colors encountered in reaching a given node set in alternating fashion. Then we demonstrate how these new forms of attractors can be embedded within greatest fixed-point computations to design solvers of parity games that run in polynomial time but are partial in that they may not decide the winning status of all nodes in the input game. Experimental results show that our partial solvers completely solve benchmarks that were constructed to challenge existing full solvers. Our partial solvers also have encouraging run times in practice. For one partial solver we prove that its run-time is at most cubic in the number of nodes in the parity game, that its output game is independent of the order in which monotone attractors are computed, and that it solves all Buechi games and weak games. We then define and study a transformation that converts partial solvers into more precise partial solvers, and we prove that this transformation is sound under very reasonable conditions on the input partial solvers. Noting that one of our partial solvers meets these conditions, we apply its transformation on 1.6 million randomly generated games and so experimentally validate that the transformation can be very effective in increasing the precision of partial solvers

The Rabin index of parity games

We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure. Colored game graphs are identified if they determine the same winning regions and strategies, for all ownership structures of nodes. The Rabin index of a parity game is the minimum of the maximal color taken over all equivalent coloring functions. We show that deciding whether the Rabin index is at least k is in PTIME for k=1 but NP-hard for all fixed k > 1. We present an EXPTIME algorithm that computes the Rabin index by simplifying its input coloring function. When replacing simple cycle with cycle detection in that algorithm, its output over-approximates the Rabin index in polynomial time. Experimental results show that this approximation yields good values in practice.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Probing near-interface ferroelectricity by conductance modulation of a nano-granular metal

The electronic functionality of thin films is governed by their interfaces. This is very important for the ferroelectric (FE) state which depends on thin-film clamping and interfacial charge transfer. Here we show that in a heterostructure consisting of a nano-granular metal and an organic FE layer of [tetrathiafulvalene]$^{+\delta}$[p-chloranil]$^{-\delta}$ the nano-granular layer's conductance provides a sensitive and non-invasive probe of the temperature-dependent dielectric properties of the FE layer. We provide a theoretical framework that is able to qualitatively reproduce the observed conductance changes taking the anisotropy of the dielectric anomaly at the paraelectric(PE)-FE phase transition into account. The approach is also suitable for observing dynamical effects close to the phase transition. Focused electron beam induced deposition as fabrication method for the nano-granular metal guarantees excellent down-scaling capabilities, so that monitoring the FE state on the lateral scale down to 20--30\,nm can be envisioned

Josephson effect in CeCoIn5CeCoIn_5 microbridges as seen via quantum interferometry

A superconducting quantum interference device (SQUID) was prepared on a micron-sized single crystal using a selected growth domain of a thin film of $CeCoIn_5$ grown by molecular beam epitaxy. SQUID voltage oscillations of good quality were obtained as well as interference effects stemming from the individual Josephson microbridges. The transport characteristics in the superconducting state exhibited several peculiarities which we ascribe to the periodic motion of vortices in the microbridges. The temperature dependence of the Josephson critical current shows good correspondence to the Ambegaokar-Baratoff relation, expected for the ideal Josephson junction. The results indicate a promising pathway to identify the type of order parameter in $CeCoIn_5$ by means of phase-sensitive measurements on microbridges.Comment: 5 pages, 4 figures, accepted to Physical Review