Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a characterization of the bisimilarity distance as the solution of a simple stochastic game. The characterization gives us an algorithm to compute the distances by applying Condon's simple policy iteration on these games. The correctness of Condon's approach, however, relies on the assumption that the games are stopping. Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games. Already other algorithms have been proposed in the literature to compute these distances, with complexity in $\textbf{UP} \cap \textbf{coUP}$ and \textbf{PPAD}. Despite the theoretical relevance, these algorithms are inefficient in practice. To the best of our knowledge, our algorithm is the first practical solution. The characterization of the probabilistic bisimilarity distance mentioned above crucially uses a dual presentation of the Hausdorff distance due to M\'emoli. As an additional contribution, in this paper we show that M\'emoli's result can be used also to prove that the bisimilarity distance bounds the difference in the maximal (or minimal) probability of two states to satisfying arbitrary $\omega$-regular properties, expressed, eg., as LTL formulas

Demographic shocks: the view from history

The paper will basically deal with four issues. The first one puts current changes or shifts into a historical comparative perspective. The second deals with "traditional" shocks or violent disturbances of the system and their consequences. The third discusses the "seismic" changes experienced in the past, attempts their measurement, and exemplifies their effects on population and society. The fourth deals with the relevance that past experience has for current changes.Demography ; Economic conditions

Two Fundamental Concepts in Skeletal Parallel Programming

We define the concepts of nesting mode and interaction mode as they arise in the description of skeletal parallel programming systems. We sugegs

Understanding Game Theory via Wireless Power Control

In this lecture note, we introduce the basic concepts of game theory (GT), a branch of mathematics traditionally studied and applied in the areas of economics, political science, and biology, which has emerged in the last fifteen years as an effective framework for communications, networking, and signal processing (SP). The real catalyzer has been the blooming of all issues related to distributed networks, in which the nodes can be modeled as players in a game competing for system resources. Some relevant notions of GT are introduced by elaborating on a simple application in the context of wireless communications, notably the power control in an interference channel (IC) with two transmitters and two receivers.Comment: Accepted for publication as lecture note in IEEE Signal Processing Magazine, 13 pages, 4 figures. The results can be reproduced using the following Matlab code: https://github.com/lucasanguinetti/ ln-game-theor