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Coinduction: Automata, Formal Proof, Companions (Invited Paper) Pous, Damien Coinduction Automata Coalgebra Formal proofs Coinduction is a mathematical tool that is used pervasively in computer science: to program and reason about infinite data-structures, to give semantics to concurrent systems, to obtain automata algorithms. We present some of these applications in automata theory and in formalised mathematics. Then we discuss recent developments on the abstract theory of coinduction and its enhancements. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Damien Pous 2019 Is Part Of LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2019.4 urn:nbn:de:0030-drops-114323 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.4 eng https://creativecommons.org/licenses/by/3.0/legalcode