Qualitative Analysis of Partially-observable Markov Decision Processes

We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability~1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDP s with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDP s with parity objectives and its subclasses

GRB 170817A-GW170817-AT 2017gfo and the observations of NS-NS, NS-WD and WD-WD mergers

The LIGO-Virgo Collaboration has announced the detection of GW170817 and has associated it with GRB 170817A. These signals have been followed after 11 hours by the optical and infrared emission of AT 2017gfo. The origin of this complex phenomenon has been attributed to a neutron star-neutron star (NS-NS) merger. In order to probe this association we confront our current understanding of the gravitational waves and associated electromagnetic radiation with four observed GRBs originating in binaries composed of different combinations NSs and white dwarfs (WDs). We consider 1) GRB 090510 the prototype of NS-NS merger leading to a black hole (BH); 2) GRB 130603B the prototype of a NS-NS merger leading to massive NS (MNS) with an associated kilonova; 3) GRB 060614 the prototype of a NS-WD merger leading to a MNS with an associated kilonova candidate; 4) GRB 170817A the prototype of a WD-WD merger leading to massive WD with an associated AT 2017gfo-like emission. None of these systems support the above mentioned association. The clear association between GRB 170817A and AT 2017gfo has led to introduce a new model based on on a new subfamily of GRBs originating from WD-WD mergers. We show how this novel model is in agreement with the exceptional observations in the optical, infrared, X- and gamma-rays of GRB 170817A-AT 2017gfo.Comment: version accepted for publication in JCAP. Missing references adde

WMAP confirming the ellipticity in BOOMERanG and COBE CMB maps

The recent study of BOOMERanG 150 GHz Cosmic Microwave Background (CMB) radiation maps have detected ellipticity of the temperature anisotropy spots independent on the temperature threshold. The effect has been found for spots up to several degrees in size, where the biases of the ellipticity estimator and of the noise are small. To check the effect, now we have studied, with the same algorithm and in the same sky region, the WMAP maps. We find ellipticity of the same average value also in WMAP maps, despite of the different sensitivity of the two experiments to low multipoles. Large spot elongations had been detected also for the COBE-DMR maps. If this effect is due to geodesic mixing and hence due to non precisely zero curvature of the hyperbolic Universe, it can be linked to the origin of WMAP low multipoles anomaly.Comment: More explanations and two references adde

Is there a common origin for the WMAP low multipole and for the ellipticity in BOOMERanG CMB maps?

We have measured the ellipticity of several degree scale anisotropies in the BOOMERanG maps of the Cosmic Microwave Background (CMB) at 150 GHz. The average ellipticity is around 2.6-2.7. The biases of the estimator of the ellipticity and for the noise are small in this case. Large spot elongation had been detected also for COBE-DMR maps. If this effect is due to geodesic mixing, it would indicate a non precisely zero curvature of the Universe which is among the discussed reasons of the WMAP low multipole anomaly. Both effects are related to the diameter of the Universe: the geodesics mixing through hyperbolic geometry, low multipoles through boundary conditions.This common reason can also be related with the origin of the the cosmological constant: the modes of vacuum fluctuations conditioned by the boundary conditions lead to a value of the cosmological constant being in remarkable agreement with the supernovae observations.Comment: Added: two co-authors and a comment on the possible relation of the discussed CMB properties with the origin of the observed value of the cosmological constan

Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games

Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus on zero-sum goals and cannot reason about scenarios where entities are endowed with different objectives. In this paper, we propose probabilistic model checking techniques for concurrent stochastic games based on Nash equilibria. We extend the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to allow reasoning about players with distinct quantitative goals, which capture either the probability of an event occurring or a reward measure. We present algorithms to synthesise strategies that are subgame perfect social welfare optimal Nash equilibria, i.e., where there is no incentive for any players to unilaterally change their strategy in any state of the game, whilst the combined probabilities or rewards are maximised. We implement our techniques in the PRISM-games tool and apply them to several case studies, including network protocols and robot navigation, showing the benefits compared to existing approaches