Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014

Social Models for Dealing with Inequalities

Production of INCASI Project H2020-MSCA-RISE-2015 GA 691004This chapter compares social models in Europe and Latin America. The goal is to study the interaction between two institutions: on the one hand, pre-distributive (ex ante) institutions, such as the structure and coverage of collective bargaining and, on the other hand, post-distributive (ex post) institutions, such as unemployment protection and social policy. Pre-distributive institutions are important for correcting inequalities in the labour market, because they introduce guidelines for egalitarian wage structures. Post-distributive institutions help to mitigate inequalities generated in the labour market. The methodology is based on statistical analysis of a series of indicators related to pre and post-distributive policies. The results present three types of model: (1) coordinated economies, typical of neo-corporatist Scandinavian countries; (2) mixed economies, typical of Mediterranean systems, and (3) uncoordinated economies, which equate to liberalism and the Latin American 'structural heterogeneity' model. It is neo-corporatist coordinated economies that generate the most pre and post-distributive equality. In turn, uncoordinated economies, and Latin American ones in particular, generate more inequalities due to highly informal employment and the weakness of their post-distributive institutions

Higher-dimensional word problems with applications to equational logic

logi

Polygraphs: From Rewriting to Higher Categories

666pp.International audiencePolygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewriting in the context of strict higher categories, adopting the abstract point of view offered by homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the coherence of algebraic structures. It is meant to be progressive, with little requirements on the background of the reader, apart from basic category theory, and is illustrated with algorithmic computations on algebraic structures. The second half introduces and studies the general notion of n-polygraph, dealing with the homotopy theory of those. It constructs the folk model structure on the category of strict higher categories and exhibits polygraphs as cofibrant objects. This allows extending to higher dimensional structures the coherence results developed in the first half

Polygraphs: From Rewriting to Higher Categories

666pp.International audiencePolygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewriting in the context of strict higher categories, adopting the abstract point of view offered by homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the coherence of algebraic structures. It is meant to be progressive, with little requirements on the background of the reader, apart from basic category theory, and is illustrated with algorithmic computations on algebraic structures. The second half introduces and studies the general notion of n-polygraph, dealing with the homotopy theory of those. It constructs the folk model structure on the category of strict higher categories and exhibits polygraphs as cofibrant objects. This allows extending to higher dimensional structures the coherence results developed in the first half