By Samson Abramsky, Jonathan Zvesper (auth.), Dirk Pattinson, Lutz Schröder (eds.)
This booklet constitutes the completely refereed post-proceedings of the eleventh overseas Workshop on Coalgebraic tools in machine technology, CMCS 2012, colocated with ETAPS 2012, held in Tallin, Estonia, in March/April 2012. the ten revised complete papers have been rigorously reviewed and chosen from 23 submissions. additionally incorporated are 3 invited talks. The papers disguise a variety of themes within the conception, logics and functions of coalgebras.
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Additional info for Coalgebraic Methods in Computer Science: 11th International Workshop, CMCS 2012, Colocated with ETAPS 2012, Tallinn, Estonia, March 31 – April 1, 2012, Revised Selected Papers
Winter Taking derivatives from (2) another time, we obtain σ + (σ · σ) + (σ 2 ) + σ + σ 2 + Xσ 2 = 0 from which, using the earlier simpliﬁcation of (σ 2 ) , and the equality (σ · σ) = σ · σ + σ (0) · σ = σ · σ + σ(1) · σ = σ · σ + σ , we obtain σ + (σ · σ + σ ) + σ · σ + σ + σ 2 + Xσ 2 = 0 (3) Taking derivatives from (3) yet another time, we obtain σ + (σ · σ) + σ + (σ · σ) + σ + (σ 2 ) + σ 2 = 0 which can be simpliﬁed, using the earlier equalities and (σ · σ) = σ · σ + σ(2) · σ = σ · σ + σ , to σ + (σ · σ + σ ) + σ + (σ · σ + σ ) + σ + σ · σ + σ 2 = 0.
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. One can easily prove that this turns S A into a ﬁnal coalgebra for the functor S × (−)A . Given any coalgebra for this functor, and an element t of its carrier set, we let t denote the value of t under the unique homomorphism of this coalgebra to S A .
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.  proved that H is a λ-accessible functor for some cardinal λ. We sharpen their result here by proving that H is ﬁnitary. Related Work. Section 4 on presentation of functors is closely related to the recent paper of A. Kurz and J. Velebil . When the preliminary version of Section 4 was presented at the PSSL Workshop in Braunschweig in April 2010, J.