<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Marcello Bonsangue</style></author><author><style face="normal" font="default" size="100%">Stefan Milius</style></author><author><style face="normal" font="default" size="100%">Alexandra Silva</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Sound and complete axiomatizations of coalgebraic language equivalence</style></title><secondary-title><style face="normal" font="default" size="100%">ACM Transactions on Computational Logic (TOCL)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://haslab.uminho.pt/sites/default/files/xana/files/1104.2803v4.pdf</style></url></related-urls></urls><number><style face="normal" font="default" size="100%">1</style></number><publisher><style face="normal" font="default" size="100%">ACM</style></publisher><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">1-51</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Coalgebras provide a uniform framework for studying dynamical systems, including several types of automata. In this article, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalized powerset construction that determinizes coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor FT, where T is a monad describing the branching of the systems (e.g., non-determinism, weights, probability, etc.), has as a quotient the rational fixpoint of the determinized type functor F, a lifting of F to the category of T-algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain nondeterministic automata in which we recover Rabinovich’s sound and complete calculus for language equivalence.&lt;/p&gt;
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