Institute of Informatics
Acta Cybernetica
Past Issues
Volume 17, Number 3, 2006
On the Complete Axiomatization for Prefix Iteration modulo Observation Congruence
# On the Complete Axiomatization for Prefix Iteration modulo Observation Congruence

**Taolue Chen,
Tingting Han,
and Jian Lu**

### Abstract (in LaTeX format)

Prefix iteration is a variation on the original binary version of the Kleene star operation $P^* Q$, obtained by restricting the first argument to be an atomic action. Aceto and Ing\'{o}lfsd\'{o}ttir provided an axiom system for observation congruence over basic CCS with prefix iteration. However hitherto the only direct completeness proof given for such a system is very long and technical. In this paper, we provide a new proof for the completeness of the axiom system in [Aceto1996], which is a considerable simplification comparing to the original proof. Thus the open problem to find a direct completeness proof is closed.

**Keywords: ** process algebra, prefix iteration, observation congruence, axiomatization, completeness.

### Full text

Available electronic editions: PDF.

### DOI

DOI is not available for this article.

### BibTeX entry
`
@article{Chen:2006:ActaCybernetica,`

author = {Taolue Chen and Tingting Han and Jian Lu},

title = {On the Complete Axiomatization for Prefix Iteration modulo Observation Congruence},

journal = {Acta Cybernetica},

year = {2006},

volume = {17},

number = {3},

pages = {471--483},

abstract = {Prefix iteration is a variation on the original binary version of the Kleene star operation $P^* Q$, obtained by restricting the first argument to be an atomic action. Aceto and Ing\'{o}lfsd\'{o}ttir provided an axiom system for observation congruence over basic CCS with prefix iteration. However hitherto the only direct completeness proof given for such a system is very long and technical. In this paper, we provide a new proof for the completeness of the axiom system in [Aceto1996], which is a considerable simplification comparing to the original proof. Thus the open problem to find a direct completeness proof is closed.},

keywords = {process algebra, prefix iteration, observation congruence, axiomatization, completeness}

}