By Davide Sangiorgi, Jan Rutten
Coinduction is a technique for specifying and reasoning approximately endless info kinds and automata with endless behaviour. lately, it has come to play an ever extra very important position within the thought of computing. it really is studied in lots of disciplines, together with strategy idea and concurrency, modal common sense and automata thought. usually, coinductive proofs reveal the equivalence of 2 items through developing an appropriate bisimulation relation among them. This number of surveys is aimed toward either researchers and Master's scholars in machine technological know-how and arithmetic and bargains with a number of facets of bisimulation and coinduction, with an emphasis on strategy thought. Seven chapters disguise the subsequent themes: heritage, algebra and coalgebra, algorithmics, common sense, higher-order languages, improvements of the bisimulation facts procedure, and chances. routines also are integrated to aid the reader grasp new material.
Contents: 1. Origins of bisimulation and coinduction (Davide Sangiorgi) — 2. An advent to (co)algebra and (co)induction (Bart Jacobs and Jan Rutten) — three. The algorithmics of bisimilarity (Luca Aceto, Anna Ingolfsdottir and Jiří Srba) — four. Bisimulation and common sense (Colin Stirling) — five. Howe’s strategy for higher-order languages (Andrew Pitts) — 6. improvements of the bisimulation evidence process (Damien Pous and Davide Sangiorgi) — 7. Probabilistic bisimulation (Prakash Panangaden)
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Extra resources for Advanced Topics in Bisimulation and Coinduction
5 Peter Aczel In mathematics, bisimulation and non-well-founded sets are made popular by Peter Aczel, notably with his book [Acz88]. Aczel is looking for mathematical foundations of processes, prompted by the work of Milner on CCS and his way of equating processes with an infinite behaviour via a bisimulation quotient. Aczel reformulates Forti and Honsell’s anti-foundation axiom X1 . In Forti and 2 We use a notation different from Forti and Honsell here. Origins of bisimulation and coinduction 2 Ñ aaa Ñ aa Ñ aa ÑÑ 0 ÑÐ Ñ 0o 1 a c ÐÐ Ð ÐÐ Ð Ð 21 b Fig.
Principia Mathematica, 3 vols. Cambridge University Press, 1910, 1912, 1913. [San09] D. Sangiorgi. On the origins of bisimulation and coinduction. ACM Transactions on Programming Languages and Systems, 31(4), 2009. [San12] D. Sangiorgi. An Introduction to Bisimulation and Coinduction. Cambridge University Press, 2012. [Sco60] D. Scott. A different kind of model for set theory. Unpublished paper, given at the 1960 Stanford Congress of Logic, Methodology and Philosophy of Science, 1960. [Sco69a] D.
G. [Coh81, MT92, Wec92]. A further step up the abstraction ladder is taken when one studies algebra with the notions and tools from category theory.