Towards Weak Bisimulation For Coalgebras

Abstract This paper contains a novel approach to observational equivalence for coalgebras. We describe how to define weak homomorphisms, weak bisimulation, and investigate the connection between them as well as the relation to the known theory of bisimulation for coalgebras. The ultimate result of the paper is the correctness-proof for a weak coinduction proof principle.

[1]  B. Jacobs,et al.  A tutorial on (co)algebras and (co)induction , 1997 .

[2]  Jirí Adámek,et al.  Abstract and Concrete Categories - The Joy of Cats , 1990 .

[3]  Michael Thomas Sanderson,et al.  Proof techniques for CCS , 1983 .

[4]  Hans-Jörg Schek,et al.  Object Orientation with Parallelism and Persistence , 1996 .

[5]  Martin Rößiger.  Coalgebras, clone theory, and modal logic , 2000 .

[6]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[7]  Věra Trnková,et al.  On descriptive classification of set-functors. II. , 1971 .

[8]  Bart Jacobs,et al.  The Coalgebraic Class Specification Language CCSL , 2001, J. Univers. Comput. Sci..

[9]  Dragan Masulovic.  Towards Coalgebraic Behaviourism , 2002, CMCS.

[10]  Jan J. M. M. Rutten,et al.  A note on coinduction and weak bisimilarity for while programs , 1998, RAIRO Theor. Informatics Appl..

[11]  Corina Ĉırstea.  Institutionalizing Coalgebraic Modal Logic , 2002, CMCS.

[12]  Jan Rothe.  A Syntactical Approach to Weak (Bi-)Simulation for Coalgebras , 2002, CMCS.

[13]  Jan J. M. M. Rutten.  Relators and Metric Bisimulations , 1998, CMCS.

[14]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[15]  Dirk Pattinson,et al.  Semantical Principles in the Modal Logic of Coalgebras , 2001, STACS.

[16]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[17]  Horst Reichel,et al.  An approach to object semantics based on terminal co-algebras , 1995, Mathematical Structures in Computer Science.

[18]  H. Gumm.  Elements Of The General Theory Of Coalgebras , 1999 .

[19]  Bart Jacobs,et al.  Objects and Classes, Co-Algebraically , 1995, Object Orientation with Parallelism and Persistence.

[20]  G. M. Kelly,et al.  A $2$-categorical approach to change of base and geometric morphisms I , 1991 .