Hostname: page-component-6898cfcb55-cbk24 Total loading time: 0 Render date: 2026-11-11T03:15:23.196Z Has data issue: false hasContentIssue false
  • English
  • Français

Pointwise extensions of GSOS-defined operations

Published online by Cambridge University Press:  25 March 2011

HELLE HVID HANSEN and
BARTEK KLIN
HELLE HVID HANSEN
Affiliation:
Technische Universiteit Eindhoven and Centrum Wiskunde & Informatica, P.O. Box 513, 5300 MB Eindhoven, The Netherlands Email: h.h.hansen@tue.nl
BARTEK KLIN
Affiliation:
University of Cambridge and University of Warsaw, 15 JJ Thomson Avenue, Cambridge CB3 0FD, U.K. Email: klin@mimuw.edu.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Final coalgebras capture system behaviours such as streams, infinite trees and processes. Algebraic operations on a final coalgebra can be defined by distributive laws (of a syntax functor Σ over a behaviour functor F). Such distributive laws correspond to abstract specification formats. One such format is a generalisation of the GSOS rules known from structural operational semantics of processes. We show that given an abstract GSOS specification ρ that defines operations σ on a final F-coalgebra, we can systematically construct a GSOS specification ρ that defines the pointwise extension σ of σ on a final FA-coalgebra. The construction relies on the addition of a family of auxiliary ‘buffer’ operations to the syntax. These buffer operations depend only on A, so the construction is uniform for all σ and F.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Special Issue 2: Coalgebraic Logic , April 2011, pp. 321 - 361
Copyright
Copyright © Cambridge University Press 2011

References

Aceto, L., Fokkink, W. J. and Verhoef, C. (2001) Structural operational semantics. In: Bergstra, J. A., Ponse, A. and Smolka, S. (eds.) Handbook of Process Algebra, Elsevier 197–292.CrossRefGoogle Scholar
Aczel, P. and Mendler, N. (1989) A final coalgebra theorem. In: Pitt, D., Rydeheard, D., Dybjer, P., Pitts, A. and Poigné, A. (eds.) Category Theory and Computer Science. Springer-Verlag Lecture Notes in Computer Science 389 357–365.CrossRefGoogle Scholar
Bartels, F. (2004) On Generalised Coinduction and Probabilistic Specification Formats, Ph.D. thesis, Vrije Universiteit Amsterdam.Google Scholar
Carton, O. (2000) Wreath product and infinite words. Journal of Pure and Applied Algebra 153 129–150.CrossRefGoogle Scholar
Hansen, H. and Klin, B. (2010) Pointwise extensions of GSOS-defined operations (extended abstract). In: CMCS 10 – Short Contributions. CWI Technical Report, SEN-1004, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands 10–11.Google Scholar
Hansen, H. H. and Rutten, J. J. M. M. (2010) Symbolic synthesis of Mealy machines from arithmetic bitstream functions. Scientific Annals of Computer Science XX 97–130.Google Scholar
Hehner, E. and Horspool, R. (1979) A new representation of the rational numbers for fast easy arithmetic. SIAM Journal on Computing 8 124–134.CrossRefGoogle Scholar
Jacobs, B. (2006) A bialgebraic review of deterministic automata, regular expressions and languages. In: Futatsugi, K., Jouannaud, J.-P. and Meseguer, J. (eds.) Algebra, Meaning and Computation: Essays dedicated to Joseph A. Goguen on the Occasion of his 65th Birthday. Springer-Verlag Lecture Notes in Computer Science 4060 375–404.CrossRefGoogle Scholar
Klin, B. (2009) Bialgebraic methods and modal logic in structural operational semantics. Information and Computation 207 237–257.CrossRefGoogle Scholar
Koblitz, N. (1984) P-adic numbers, p-adic Analysis, and Zeta-Functions, second edition, Graduate Texts in Mathematics, Springer-Verlag.CrossRefGoogle Scholar
Lambek, J. (1968) A fixpoint theorem for complete categories. Mathematische Zeitschrift 103 (2)151–161.CrossRefGoogle Scholar
Lenisa, M., Power, J. and Watanabe, H. (2004) Category theory for operational semantics. Theoretical Computer Science 327 (1-2) 135–154.CrossRefGoogle Scholar
Pin, J.-E. and Weil, P. (2002) The wreath product principle for ordered semigroups. Communications in Algebra 30 5677–5713.CrossRefGoogle Scholar
Rutten, J. (1991) Coalgebra, concurrency and control. CWI Research Report SEN-9921, Centrum Wiskunde & Informatica, Amsterdam, The NetherlandsGoogle Scholar
Rutten, J. (2000) Universal coalgebra: a theory of systems. Theoretical Computer Science 249 3–80.CrossRefGoogle Scholar
Rutten, J. (2003) Behavioural differential equations: a coinductive calculus of streams, automata and power series. Theoretical Computer Science 308 (1)1–53.CrossRefGoogle Scholar
Rutten, J. (2006) Algebraic specification and coalgebraic synthesis of Mealy machines. In: Proceedings of the 2nd International Workshop on Formal Aspects of Component Software (FACS 2005). Electronic Notes in Theoretical Computer Science 160 305–319.CrossRefGoogle Scholar
Rutten, J. and Turi, D. (1994) Initial algebra and final coalgebra semantics for concurrency. In: de Bakker, J., de Roever, W.-P. and Rozenberg, G. (eds.) A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium. Springer-Verlag Lecture Notes in Computer Science 803 530–582.CrossRefGoogle Scholar
Straubing, H. (1989) The wreath product and its applications. In: Formal Properties of Finite Automata and Applications. Springer-Verlag Lecture Notes in Computer Science 386 15–24.CrossRefGoogle Scholar
Turi, D. and Plotkin, G. (1997) Towards a mathemathical operational semantics. In: Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science (LICS 1997), IEEE Computer Society 280–291.Google Scholar
Worrell, J. (2005) On the final sequence of a finitary set functor. Theoretical Computer Science 338 184–199.CrossRefGoogle Scholar