TY - JOUR
T1 - Leanest quasi-orderings
AU - Dershowitz, Nachum
AU - Castedo Ellerman, E.
N1 - Funding Information:
∗ Corresponding author. E-mail addresses: [email protected] (N. Dershowitz), [email protected] (E. Castedo Ellerman). 1 Supported in part by the Israel Science Foundation (Grant No. 250/05).
PY - 2007/4
Y1 - 2007/4
N2 - A convenient method for defininga quasi-ordering, such as those used for proving termination of rewriting, is to choose the minimum of a set of quasi-orderings satisfying some desired traits. Unfortunately, a minimum in terms of set inclusion can be non-existent even when an intuitive "minimum" exists. We suggest an alternative to set inclusion, called "leanness", show that leanness is a partial order on quasi-orderings, and provide sufficient conditions for the existence of a "leanest" member of a set of total well-founded quasi-orderings.
AB - A convenient method for defininga quasi-ordering, such as those used for proving termination of rewriting, is to choose the minimum of a set of quasi-orderings satisfying some desired traits. Unfortunately, a minimum in terms of set inclusion can be non-existent even when an intuitive "minimum" exists. We suggest an alternative to set inclusion, called "leanness", show that leanness is a partial order on quasi-orderings, and provide sufficient conditions for the existence of a "leanest" member of a set of total well-founded quasi-orderings.
KW - Lexicographic path ordering
KW - Quasi-ordering
KW - Well-quasi-ordering
UR - http://www.scopus.com/inward/record.url?scp=84856018583&partnerID=8YFLogxK
U2 - 10.1016/j.ic.2006.10.007
DO - 10.1016/j.ic.2006.10.007
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AN - SCOPUS:84856018583
SN - 0890-5401
VL - 205
SP - 535
EP - 556
JO - Information and Computation
JF - Information and Computation
IS - 4
ER -