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

Issue		RAIRO-Theor. Inf. Appl. Volume 35, Number 1, January-February 2001 Coalgebraic Methods in Computer Science


Page(s)		1 - 29
DOI		10.1051/ita:2001107

DOI: 10.1051/ita:2001107

Theoret. Informatics Appl. 35, 1-29 (2001)

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

Corina Cîrstea

Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, U.K.; (corina.cirstea@comlab.ox.ac.uk)

( Accepted April 25, 2001.)

Abstract
We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system states and the observations that can be made about these states is specified using liftings of the coalgebraic 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 the associated notions of satisfaction abstracting away observationally indistinguishable, respectively unreachable states, and with the resulting proof techniques employing coinduction, respectively induction.

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