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Integrating Observational and Computational Features in the Specification of State-Based, Dynamical Systems

Published online by Cambridge University Press:  15 April 2002

Corina Cîrstea
Corina Cîrstea*
Affiliation:
Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, U.K.; e-mail: corina.cirstea@comlab.ox.ac.uk
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Abstract

We present an abstract equational framework for the specification of systems having bothobservational and computational features. Our approach is based on a clear separation between the twocategories of features, and uses algebra, respectively coalgebra to formalise them. This yields acoalgebraically-defined notion of observational indistinguishability, as well as an algebraically-definednotion of reachability under computations. The relationship between the computations yielding new systemstates and the observations that can be made about these states is specified using liftings of thecoalgebraic structure of state spaces to a coalgebraic structure on computations over these state spaces.Also, correctness properties of system behaviour are formalised using equational sentences, with theassociated notions of satisfaction abstracting away observationally indistinguishable, respectivelyunreachable states, and with the resulting prooftechniques employing coinduction, respectively induction.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 1: Coalgebraic Methods in Computer Science , January 2001 , pp. 1 - 29
Copyright
© EDP Sciences, 2001

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References

F. Borceux, Handbook of Categorial Algebra, Vol. II. CUP, Cambridge (1994).
C. Cîrstea, A Coequational Approach to Specifying Behaviours, edited by B. Jacobs and J. Rutten, Coalgebraic Methods in Computer Science. Elsevier Science, Electron. Notes Theor. Comput. Sci. 19 (1999) 173-194.
C. Cîrstea, An Algebra-Coalgebra Framework for System Specification, edited by H. Reichel, Coalgebraic Methods in Computer Science. Elsevier Science, Electron. Notes Theor. Comput. Sci. 33 (2000) 81-112.
C. Cîrstea, Integrating Observations and Computations in the Specification of State-Based, Dynamical Systems, Ph.D. Thesis. University of Oxford (2000) http://www.comlab.ox.ac.uk/oucl/work/corina.cirstea/thesis.html
A. Corradini, A Completeness Result for Equational Deduction in Coalgebraic Specification, edited by F. Parisi-Presicce, Recent Trends in Algebraic Development Techniques. Springer, Lecture Notes in Comput. Sci. 1376 (1998) 190-205.
A. Corradini, R. Heckel and U. Montanari, From SOS Specifications to Structured Coalgebras: How to Make Bisimulation a Congruence, edited by B. Jacobs and J. Rutten, Coalgebraic Methods in Computer Science. Elsevier Science, Electron. Notes Theor. Comput. Sci. 19 (1999) 149-172.
R. Diaconescu, Behavioural Coherence in Object-Oriented Algebraic Specification, Technical Report IS-RR-98-0017F. Japan Advanced Institute for Science and Technology (1998).
Goguen, J. and Burstall, R., Institutions: Abstract Model Theory for Specification and Programming. J. ACM 39 (1992) 95-146. CrossRef
Goguen, J. and Malcolm, G., Hidden Agenda, A. Theoret. Comput. Sci. 245 (2000) 55-101. CrossRef
R. Hennicker and M. Bidoit, Observational Logic, in Proc. AMAST '98. Springer, Lecture Notes in Comput. Sci. 1548 (1999) 263-277.
R. Hennicker and A. Kurz, (Ω,Ξ)-Logic: On the Algebraic Extension of Coalgebraic Specifications, edited by B. Jacobs, L. Moss, H. Reichel and J. Rutten, Coalgebraic Methods in Computer Science. Elsevier Science, Electron. Notes Theor. Comput. Sci. 19 (1999) 195-211.
B. Jacobs, Objects and Classes, Coalgebraically, edited by B. Freitag, C.B. Jones, C. Lengauer and H.-J. Schek, Object Orientation with Parallelism and Persistence. Kluwer Academic Publishers (1996) 83-103.
B. Jacobs, Invariants, Bisimulations and the Correctness of Coalgebraic Refinements, edited by M. Johnson, Algebraic Methodology and Software Technology. Springer, Lecture Notes in Comput. Sci. 1349 (1997) 276-291.
Padawitz, P., Swinging Types = Functions + Relations + Transition Systems. Theoret. Comput. Sci. 243 (2000) 93-165. CrossRef
Reichel, H., Approach, An to Object Semantics Based on Terminal Coalgebras. Math. Structures Comput. Sci. 5 (1995) 129-152. CrossRef
G. Rosu and J. Goguen, Hidden Congruent Deduction, edited by R. Caferra and G. Salzer, Automated Deduction in Classical and Non-Classical Logics. Springer, Lecture Notes in Comput. Sci. 1761 (2000) 251-266.
Rutten, J., Universal Coalgebra: A Theory of Systems. Theoret. Comput. Sci. 249 (2000) 3-80. CrossRef
D. Turi and G. Plotkin, Towards a Mathematical Operational Semantics, in Proc. LICS (1997) 280-291.