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» Algorithms for Ordinal Arithmetic
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CIE
2007
Springer
13 years 10 months ago
The Complexity of Quickly ORM-Decidable Sets
Abstract. The Ordinal Register Machine (ORM) is one of several different machine models for infinitary computability. We classify, by complexity, the sets that can be decided quic...
Joel David Hamkins, David Linetsky, Russell G. Mil...
TALG
2008
81views more  TALG 2008»
13 years 4 months ago
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
We introduce a new notion of embedding, called minimum-relaxation ordinal embedding, parallel to the standard notion of minimum-distortion (metric) embedding. In an ordinal embedd...
Noga Alon, Mihai Badoiu, Erik D. Demaine, Martin F...
ALGORITHMICA
1999
99views more  ALGORITHMICA 1999»
13 years 4 months ago
Evolutionary Trees and Ordinal Assertions
Sequence data for a group of species is often summarized by a distance matrix M where M[s, t] is the dissimilarity between the sequences of species s and t. An ordinal assertion is...
Paul E. Kearney, Ryan Hayward, Henk Meijer
JSYML
2006
87views more  JSYML 2006»
13 years 4 months ago
Permutations and wellfoundedness: the true meaning of the bizarre arithmetic of Quine's NF
It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-...
Thomas Forster
FMCAD
2004
Springer
13 years 10 months ago
Integrating Reasoning About Ordinal Arithmetic into ACL2
Abstract. Termination poses one of the main challenges for mechanically verifying infinite state systems. In this paper, we develop a powerful and extensible framework based on th...
Panagiotis Manolios, Daron Vroon