POPL 2019
Sun 13 - Sat 19 January 2019 Cascais, Portugal
Fri 18 Jan 2019 14:29 - 14:51 at Sala I - Semantics Chair(s): Noam Zeilberger

Many analysis and verifications tasks, such as static program analyses and model-checking for temporal logics, reduce to the solution of systems of equations over suitable lattices. Inspired by recent work on lattice-theoretic progress measures, we develop a game-theoretical approach to the solution of systems of monotone equations over lattices, where for each single equation either the least or greatest solution is taken. A simple parity game, referred to as fixpoint game, is defined that provides a correct and complete characterisation of the solution of systems of equations over continuous lattices, a quite general class of lattices widely used in semantics. For powerset lattices the fixpoint game is intimately connected with classical parity games for $\mu$-calculus model-checking, whose solution can exploit as a key tool Jurdziński’s small progress measures. We show how the notion of progress measure can be naturally generalised to fixpoint games over continuous lattices and we prove the existence of small progress measures. Our results lead to a constructive formulation of progress measures as (least) fixpoints. We refine this characterisation by introducing the notion of selection that allows one to constrain the plays in the parity game, enabling an effective (and possibly efficient) solution of the game, and thus of the associated verification problem. We also propose a logic for specifying the moves of the existential player that can be used to systematically derive simplified equations for efficiently computing progress measures. We discuss potential applications to the model-checking of latticed $\mu$-calculi.

 Slides (talk-online.pdf) 3.41MiB

#### Fri 18 JanDisplayed time zone: Belfast change

 13:45 - 14:51 SemanticsResearch Papers at Sala I Chair(s): Noam Zeilberger University of Birmingham, UK 13:4522mTalk Better Late Than Never: A Fully Abstract Semantics for Classical ProcessesResearch PapersWen Kokke University of Edinburgh, Fabrizio Montesi University of Southern Denmark, Marco Peressotti University of Southern Denmark Link to publication DOI Media Attached 14:0722mTalk Diagrammatic Algebra: From Linear to Concurrent SystemsResearch PapersFilippo Bonchi University of Pisa, Joshua Holland University of Southampton, Robin Piedeleu University of Oxford, Pawel Sobocinski University of Southampton, Fabio Zanasi University College London Link to publication DOI Media Attached 14:2922mTalk Fixpoint Games on Continuous LatticesResearch PapersPaolo Baldan University of Padova, Barbara König University of Duisburg-Essen, Christina Mika-Michalski University of Duisburg-Essen, Tommaso Padoan University of Padova Link to publication DOI Media Attached File Attached