Download Advanced Topics in Bisimulation and Coinduction by Davide Sangiorgi, Jan Rutten PDF

By Davide Sangiorgi, Jan Rutten

Coinduction is a technique for specifying and reasoning approximately limitless information varieties and automata with endless behaviour. lately, it has come to play an ever extra very important function within the conception of computing. it really is studied in lots of disciplines, together with technique conception and concurrency, modal common sense and automata concept. usually, coinductive proofs exhibit the equivalence of 2 gadgets through developing an appropriate bisimulation relation among them. This selection of surveys is aimed toward either researchers and Master's scholars in computing device technological know-how and arithmetic and bargains with a number of elements of bisimulation and coinduction, with an emphasis on approach thought. Seven chapters hide the next subject matters: heritage, algebra and coalgebra, algorithmics, good judgment, higher-order languages, improvements of the bisimulation facts approach, and chances. routines also are incorporated 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 technique for higher-order languages (Andrew Pitts) — 6. improvements of the bisimulation evidence procedure (Damien Pous and Davide Sangiorgi) — 7. Probabilistic bisimulation (Prakash Panangaden)

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Extra resources for Advanced Topics in Bisimulation and Coinduction

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The Y-combinator in Scott’s lambda-calculus models. Symposium on Theory of Programming, University of Warwick, unpublished (A revised version: Research Report CS-RR-013, Department of Computer Science, University of Warwick, June 1976), 1970. [Par79] D. Park. On the semantics of fair parallelism. In Proceedings of Abstract Software Specifications, Copenhagen Winter School, Lecture Notes in Computer Science, pages 504–526. Springer, 1979. [Par81a] D. Park. Concurrency on automata and infinite sequences.

It is easy to see that they are bisimilar. 2, are quite different. ) What really makes Mirimanoff’s isomorphism different from bisimulation is that Mirimanoff fails to promote isomorphism to equality for sets. For instance, the sets A D fBg and B D fAg are isomorphic but not equal, hence the set fA, Bg has two elements and is not isomorphic to the set fAg or to the set fBg, which have only one element. To identify isomorphism and equality, the clause of isomorphism, in establishing the ‘perfect correspondence’ between the elements of two isomorphic sets, should take into account the collapse given by isomorphism itself.

Mir20] D. Mirimanoff. Remarques sur la th´eorie des ensembles et les antinomies cantoriennes II. L’Enseignement Math´ematique, 21:29–52, 1920. F. Moore. Gedanken experiments on sequential machines. Automata Studies, Annals of Mathematics Series, 34:129–153, 1956. H. Morris. Lambda-calculus models of programming languages. PhD thesis, MIT, project MAC, Dec. 1968. N. Moschovakis. Elementary Induction on Abstract Structures, volume 77 of Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam, 1974.

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