Integrating observational and computational features in the specification of state-based, dynamical systems
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 1, pp. 1-29.

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.

Classification : 18C10,  03C65,  68Q55,  68N30
@article{ITA_2001__35_1_1_0,
author = {C{\^\i}rstea, Corina},
title = {Integrating observational and computational features in the specification of state-based, dynamical systems},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {1--29},
publisher = {EDP-Sciences},
volume = {35},
number = {1},
year = {2001},
zbl = {0987.18004},
mrnumber = {1845873},
language = {en},
url = {http://www.numdam.org/item/ITA_2001__35_1_1_0/}
}
Cîrstea, Corina. Integrating observational and computational features in the specification of state-based, dynamical systems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 1, pp. 1-29. http://www.numdam.org/item/ITA_2001__35_1_1_0/

[1] F. Borceux, Handbook of Categorial Algebra, Vol. II. CUP, Cambridge (1994).

[2] 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. | MR 1689455 | Zbl 0918.68063

[3] 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. | MR 1787575 | Zbl 0966.68129

[4] 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

[5] 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. | MR 1656751 | Zbl 0903.08007

[6] 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. | MR 1689454 | Zbl 0918.68065

[7] R. Diaconescu, Behavioural Coherence in Object-Oriented Algebraic Specification, Technical Report IS-RR-98-0017F. Japan Advanced Institute for Science and Technology (1998).

[8] J. Goguen and R. Burstall, Institutions: Abstract Model Theory for Specification and Programming. J. ACM 39 (1992) 95-146. | MR 1147298 | Zbl 0799.68134

[9] J. Goguen and G. Malcolm, A Hidden Agenda. Theoret. Comput. Sci. 245 (2000) 55-101. | MR 1784537 | Zbl 0946.68070

[10] R. Hennicker and M. Bidoit, Observational Logic, in Proc. AMAST '98. Springer, Lecture Notes in Comput. Sci. 1548 (1999) 263-277.

[11] R. Hennicker and A. Kurz, $\left(\Omega ,\Xi \right)$-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. | MR 1689456 | Zbl 0918.68064

[12] 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.

[13] 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.

[14] P. Padawitz, Swinging Types = Functions + Relations + Transition Systems. Theoret. Comput. Sci. 243 (2000) 93-165. | MR 1776158 | Zbl 0947.68098

[15] H. Reichel, An Approach to Object Semantics Based on Terminal Coalgebras. Math. Structures Comput. Sci. 5 (1995) 129-152. | MR 1368919 | Zbl 0854.18006

[16] G. Roşu 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. | MR 1790867 | Zbl 0964.68083

[17] J. Rutten, Universal Coalgebra: A Theory of Systems. Theoret. Comput. Sci. 249 (2000) 3-80. | MR 1791953 | Zbl 0951.68038

[18] D. Turi and G. Plotkin, Towards a Mathematical Operational Semantics, in Proc. LICS (1997) 280-291.