Abstract models of transfinite reductions
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Standard
Abstract models of transfinite reductions. / Bahr, Patrick.
Proceedings of the 21st International Conference on Rewriting Techniques and Applications. ed. / Christopher Lynch. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010. p. 49-66 (Leibniz International Proceedings in Informatics, Vol. 6).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - GEN
T1 - Abstract models of transfinite reductions
AU - Bahr, Patrick
PY - 2010
Y1 - 2010
N2 - We investigate transfinite reductions in abstract reduction systems. To this end, we study two abstract models for transfinite reductions: a metric model generalising the usual metric approach to infinitary term rewriting and a novel partial order model. For both models we distinguish between a weak and a strong variant of convergence as known from infinitary term rewriting. Furthermore, we introduce an axiomatic model of reductions that is general enough to cover all of these models of transfinite reductions as well as the ordinary model of finite reductions. It is shown that, in this unifying axiomatic model, many basic relations between termination and confluence properties known from finite reductions still hold. The introduced models are applied to term rewriting but also to term graph rewriting. We can show that for both term rewriting as well as for term graph rewriting the partial order model forms a conservative extension to the metric model.
AB - We investigate transfinite reductions in abstract reduction systems. To this end, we study two abstract models for transfinite reductions: a metric model generalising the usual metric approach to infinitary term rewriting and a novel partial order model. For both models we distinguish between a weak and a strong variant of convergence as known from infinitary term rewriting. Furthermore, we introduce an axiomatic model of reductions that is general enough to cover all of these models of transfinite reductions as well as the ordinary model of finite reductions. It is shown that, in this unifying axiomatic model, many basic relations between termination and confluence properties known from finite reductions still hold. The introduced models are applied to term rewriting but also to term graph rewriting. We can show that for both term rewriting as well as for term graph rewriting the partial order model forms a conservative extension to the metric model.
KW - Faculty of Science
KW - infinitary rewriting
KW - metric
KW - partial order
KW - abstract reduction system
KW - axiomatic
KW - term rewriting
KW - graph rewriting
U2 - 10.4230/LIPIcs.RTA.2010.49
DO - 10.4230/LIPIcs.RTA.2010.49
M3 - Article in proceedings
T3 - Leibniz International Proceedings in Informatics
SP - 49
EP - 66
BT - Proceedings of the 21st International Conference on Rewriting Techniques and Applications
A2 - Lynch, Christopher
PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Y2 - 11 July 2010 through 13 July 2010
ER -
ID: 20876656