# Rational Operational Models

Milius S, Bonsangue M, Myers R, Rot J (2013)

**Publication Type:** Conference contribution

**Publication year:** 2013

### Journal

**Publisher:** Elsevier BV

**Edited Volumes:** Electronic Notes in Theoretical Computer Science

**Series:** Electronic Notes in Theoretical Computer Science

**City/Town:** Berlin München

**Book Volume:** 298

**Pages Range:** 257-282

**Conference Proceedings Title:** Proc. of the Twenty-ninth Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIX

**URI:** https://www8.cs.fau.de/~milius/publications/papers.html

**DOI:** 10.1016/j.entcs.2013.09.017

### Abstract

GSOS is a specification format for well-behaved operations on transition systems. Aceto introduced a restriction of this format, called simple GSOS, which guarantees that the associated transition system is locally finite, i.e. every state has only finitely many different descendent states (i.e. states reachable by a sequence of transitions). The theory of coalgebras provides a framework for the uniform study of systems, including labelled transition systems but also, e.g. weighted transition systems and (non-)deterministic automata. In this context GSOS can be studied at the general level of distributive laws of syntax over behaviour. In the present paper we generalize Aceto's result to the setting of coalgebras by restricting abstract GSOS to bipointed specifications. We show that the operational model of a bipointed specification is locally finite, even for specifications with infinitely many operations which have finite dependency. As an example, we derive a concrete format for operations on regular languages and obtain for free that regular expressions have finitely many derivatives modulo the equations of join semilattices. © 2013 Elsevier B.V.

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### How to cite

**APA:**

Milius, S., Bonsangue, M., Myers, R., & Rot, J. (2013). Rational Operational Models. In *Proc. of the Twenty-ninth Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIX* (pp. 257-282). Berlin München: Elsevier BV.

**MLA:**

Milius, Stefan, et al. "Rational Operational Models." *Proceedings of the Proc. of the Twenty-ninth Conference on the Mathematical Foundations of Programming Semantics, MFPS XXIX* Berlin München: Elsevier BV, 2013. 257-282.

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