eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2010-12-14
284
295
10.4230/LIPIcs.FSTTCS.2010.284
article
Uniqueness of Normal Forms is Decidable for Shallow Term Rewrite Systems
Radcliffe, Nicholas
Verma, Rakesh M.
Uniqueness of normal forms (UN=) is an important property of term rewrite systems. UN= is decidable for ground (i.e., variable-free) systems and undecidable in general. Recently it was shown to be decidable for linear, shallow systems. We generalize this previous result and show that this property is decidable for shallow rewrite systems, in contrast to confluence, reachability and other properties, which are all undecidable for flat systems. Our result is also optimal in some sense, since we prove that the UN= property is undecidable for two superclasses of flat systems: left-flat, left-linear systems in which right-hand sides are of depth at most two and right-flat, right-linear systems in which left-hand sides are of depth at most two.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol008-fsttcs2010/LIPIcs.FSTTCS.2010.284/LIPIcs.FSTTCS.2010.284.pdf
term rewrite systems
uniqueness of normal forms
decidability
shallo w rewrite systems
flat rewrite systems