By Davide Sangiorgi, Jan Rutten

ISBN-10: 1107004977

ISBN-13: 9781107004979

Coinduction is a technique for specifying and reasoning approximately countless facts kinds and automata with countless behaviour. lately, it has come to play an ever extra very important function within the concept of computing. it really is studied in lots of disciplines, together with method thought and concurrency, modal common sense and automata concept. quite often, coinductive proofs show the equivalence of 2 items via developing an appropriate bisimulation relation among them. This choice of surveys is aimed toward either researchers and Master's scholars in machine technological know-how and arithmetic and offers with a number of elements of bisimulation and coinduction, with an emphasis on procedure idea. Seven chapters hide the subsequent themes: heritage, algebra and coalgebra, algorithmics, good judgment, higher-order languages, improvements of the bisimulation facts procedure, and possibilities. workouts also are integrated to aid the reader grasp new material.

Contents: 1. Origins of bisimulation and coinduction (Davide Sangiorgi) — 2. An creation 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 good judgment (Colin Stirling) — five. Howe’s procedure for higher-order languages (Andrew Pitts) — 6. improvements of the bisimulation evidence strategy (Damien Pous and Davide Sangiorgi) — 7. Probabilistic bisimulation (Prakash Panangaden)

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N. Moschovakis. The next admissible set. Journal of Symbolic Logic, 36:108–120, 1971. [Bir48] G. Birkhoff. Lattice Theory (Revised Edition). Volume 25 of American Mathematical Society Colloquium Publications. American Mathematical Society, 1948. [Bli77] A. Blikle. A comparative review of some program verification methods. In Jozef Gruska, editor, 6th Symposium on Mathematical Foundations of 32 [BM96] [Bof68] [Bof69] [Bof72] [Bou50] [BR73] [Bra78] [BRV01] [Buc94] [Bur75] [Cad72] [CC79] [Cla77] [Dev63] [dR77] [Ehr61] [FH83] [Fin26] Davide Sangiorgi Computer Science (MFCS’77), volume 53 of Lecture Notes in Computer Science, pages 17–33.

Similar versions are also given by Devid´e [Dev63], Pasini [Pas74], Cadiou [Cad72], Cousot and Cousot [CC79]. A related theorem also appears in Bourbaki [Bou50]. Bibliography [Acz88] P. Aczel. Non-Well-Founded Sets. CSLI Lecture Notes, no. 14, 1988. [AIS12] L. Aceto, A. Ingolfsdottir, and J. Srba. The algorithmics of bisimilarity. Chapter 3 of this volume. N. Arden. Delayed logic and finite state machines. In Theory of Computing Machine Design, pages 1–35. University of Michigan Press, 1960. W.

6 Jon Barwise Aczel’s original motivation for the study on non-well-founded sets is to provide set-theoretic models for CCS. e. human spoken) languages [BE87]. Further, Barwise develops a theory of non-well-founded sets that is not based on the relationship between sets and graph theory as Aczel, but, instead, on systems of equations. The axiom AFA becomes a requirement that appropriate systems of equations have a unique solution. To understand this point consider that, as the purely reflexive set can be seen as the solution to the equation x D fxg, so all non-well-founded sets arise from systems of equations with variables on the left-hand side, and well-founded sets possibly containing such variables on the right-hand side.

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