By Samson Abramsky, Jonathan Zvesper (auth.), Dirk Pattinson, Lutz Schröder (eds.)
This publication constitutes the completely refereed post-proceedings of the eleventh overseas Workshop on Coalgebraic equipment in computing device technology, CMCS 2012, colocated with ETAPS 2012, held in Tallin, Estonia, in March/April 2012. the ten revised complete papers have been conscientiously reviewed and chosen from 23 submissions. additionally incorporated are 3 invited talks. The papers disguise quite a lot of issues within the idea, logics and purposes of coalgebras.
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The final coalgebra structure can be defined using a generalisation of the notion of Brzozowski derivatives, originally introduced for regular expressions and languages, as follows. Given a coalgebra (X, (o, δ) : X → S × X A ), and an element x ∈ X, we write xa for δ(x)(a), and call it the a-derivative of x; furthermore, we call o(x) the output value of x. The set S A can now be given a S × (−)A -coalgebra structure by defining, for σ ∈ S A , a ∈ A and w ∈ A∗ , σa (w) := σ(a · w) and by setting, furthermore, o(σ) := σ(λ), where λ is the empty word.
Relational and partial variable sets and basic predicate logic. J. Symbolic Logic 61(3), 843–872 (1996) 16. : Generic trace semantics via coinduction. Log. Meth. Comput. Sci. 3(4) (2007) 17. : Simulations in coalgebras. Theor. Comput. Sci. 327(1-2), 71–108 (2004) 18. : Trace semantics for coalgebras. In: Coalgebraic Methods in Computer Science, CMCS 2004. ENTCS, vol. 106, pp. 167–184 (2004) 19. : Mobile Processes in Bigraphs. PhD thesis, University of Cambridge (2006) 20. : Bisimulation from open maps.
Power [9]. We then turn to an endofunctor of the category CMS of complete metric spaces of special interest: the Hausdorff D. Pattinson and L. ): CMCS 2012, LNCS 7399, pp. 51–70, 2012. c IFIP International Federation for Information Processing 2012 52 J. Ad´ amek, S. S. Moss functor H assigning to every space X the space H X of all non-empty compact subsets of X with the Hausdorff metric. F. van Breugel et al. [8] proved that H is a λ-accessible functor for some cardinal λ. We sharpen their result here by proving that H is finitary.
