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Abstract: Series-parallel orders are defined as the least class of partial orders containing the one-element order and closed by ordinal sum and disjoint union. From this inductive denition, it is almost immediate that any series-parallel order may be represented by an algebraic expression, which is unique up to the associativivity of ordinal sum and to the associativivity and commutativity of disjoint union. In this paper, we introduce a rewrite system acting on these algebraic expressions that... (Update)
Context of citations to this paper: More
...equivalent to system SBVc. Retore got his rewriting rules from a study of the inclusion relation for series parallel orders, in [4]. Since series parallel orders are at the basis of my definition of structures, Retore s result and mine are similar because they come from...
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BibTeX entry: (Update)
Denis Bechet, Philippe de Groote, and Christian Retore. A complete axiomatisation of the inclusion of series-parallel partial orders. In H. Comon, editor, Rewriting Techniques and Applications, RTA`97, volume 1232 of LNCS, pages 230--240. Springer Verlag, 1997. http://citeseer.ist.psu.edu/article/bechet97complete.html More
@inproceedings{ bechet97complete,
author = "Denis B\'echet and Philippe de Groote and Christian Retor\'e",
title = "A complete axiomatisation for the inclusion of series-parallel partial orders",
booktitle = "Procceedings of the Eighth International Conference on Rewriting Techniques and Applications",
address = "Sitges, Spain",
year = "1997",
url = "citeseer.ist.psu.edu/article/bechet97complete.html" }
Citations (may not include all citations):74 The recognition of Series-Parallel digraphs (context) - Lawler, Tarjan et al. - 1982
36 Algorithmic graph theory and perfect graphs (context) - Golumbic - 1980
35 Pomset logic: a non-commutative extension of classical linea.. - Retor - 1997
5 quents Ordonn#s (context) - Retor, seaux - 1993
5 Partially commutative linear logic: sequent calculus and pha.. - de Groote - 1996
4 Perfect matchings and series-parallel graphs: multiplicative.. - Retor - 1996
4 volume 255 of NATO ASI series C (context) - Rival, Algorithms - 1989
2 Computationally tractable classes of ordered sets (context) - hring - 1989
The graph only includes citing articles where the year of publication is known.
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