Weak convergence and uniform normalization in infinitary rewriting

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Abstract

We study infinitary term rewriting systems containing finitely many rules. For these, we show that if a weakly convergent reduction is not strongly convergent, it contains a term that reduces to itself in one step (but the step itself need not be part of the reduction). Using this result, we prove the starkly surprising result that for any orthogonal system with finitely many rules, the system is weakly normalizing under weak convergence if{f} it is strongly normalizing under weak convergence if{f} it is weakly normalizing under strong convergence if{f} it is strongly normalizing under strong convergence. As further corollaries, we derive a number of new results for weakly convergent rewriting: Systems with finitely many rules enjoy unique normal forms, and acyclic orthogonal systems are confluent. Our results suggest that it may be possible to recover some of the positive results for strongly convergent rewriting in the setting of weak convergence, if systems with finitely many rules are considered. Finally, we give a number of counterexamples showing failure of most of the results when infinite sets of rules are allowed.
OriginalsprogEngelsk
TitelProceedings of the 21st International Conference on Rewriting Techniques and Applications,
RedaktørerChristopher Lynch
Antal sider14
ForlagSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publikationsdato2010
Sider311-324
ISBN (Elektronisk)978-3-939897-18-7
DOI
StatusUdgivet - 2010
Begivenhed21st International Conference on Rewriting Techniques and Applications - Edinburgh, Storbritannien
Varighed: 11 jul. 201013 jul. 2010

Konference

Konference21st International Conference on Rewriting Techniques and Applications
Land/OmrådeStorbritannien
ByEdinburgh
Periode11/07/201013/07/2010
NavnLeibniz International Proceedings in Informatics (LIPIcs)
Vol/bind6
ISSN1868-8969

Citationsformater