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QRB-Domains and the Probabilistic Powerdomain

Jean Goubault-Larrecq.

Is there any Cartesian-closed category of continuous domains that would be closed under Jones and Plotkin's probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higher-order languages. We relax the question, and look for&nbsp;[&hellip;]

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Forward Analysis for WSTS, Part II: Complete WSTS

Alain Finkel ; Jean Goubault-Larrecq.

We describe a simple, conceptual forward analysis procedure for infinity-complete WSTS S. This computes the so-called clover of a state. When S is the completion of a WSTS X, the clover in S is a finite description of the downward closure of the reachability set. We show that such completions are&nbsp;[&hellip;]

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The Ho-Zhao Problem

Weng Kin Ho ; Jean Goubault-Larrecq ; Achim Jung ; Xiaoyong Xi.

Given a poset $P$, the set, $\Gamma(P)$, of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory $\mathbf{C}$ of $\mathbf{Pos}_d$ (the category of posets and Scott-continuous maps) is said to be $\Gamma$-faithful if for any posets $P$ and $Q$ in $\mathbf{C}$, $\Gamma(P)&nbsp;[&hellip;]

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A Few Notes on Formal Balls

Jean Goubault-Larrecq ; Kok Min Ng.

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its $d$-Scott topology; for standard quasi-metric spaces,&nbsp;[&hellip;]

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Forward Analysis for WSTS, Part III: Karp-Miller Trees

Michael Blondin ; Alain Finkel ; Jean Goubault-Larrecq.

This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and "Forward Analysis for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward&nbsp;[&hellip;]

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