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Integrating observational and computational features in the specification of state-based, dynamical systems

Integrating observational and computational features in the specification of state-based, dynamical systems
Integrating observational and computational features in the specification of state-based, dynamical systems
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.
algebraic specification, coalgebraic specification
0988-3754
1-29
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Reichel, H.
8dc80504-8da3-42d9-90b9-4f1f71a7994f
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Reichel, H.
8dc80504-8da3-42d9-90b9-4f1f71a7994f

Cirstea, Corina, Reichel, H.(ed.) (2001) Integrating observational and computational features in the specification of state-based, dynamical systems Theoretical Informatics and Applications, 35, (1), pp. 1-29.

Record type: Article

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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Published date: 2001
Keywords: algebraic specification, coalgebraic specification
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 259128
URI: http://eprints.soton.ac.uk/id/eprint/259128
ISSN: 0988-3754
PURE UUID: 7ae42c17-6e83-4e28-8384-fad38bb548db

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Date deposited: 12 Mar 2004
Last modified: 18 Jul 2017 09:25

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Contributors

Author: Corina Cirstea
Editor: H. Reichel

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