Logic in Computer Science, Symposium on (2003)
June 22, 2003 to June 25, 2003
Bakhadyr Khoussainov , University of Auckland, New Zealand
Sasha Rubin , University of Auckland, New Zealand
Frank Stephan , University of Heidelberg, Germany
We investigate partial orders that are computable, in a precise sense, by finite automata. Our emphasis is on trees and linear orders. We study the relationship between automatic linear orders and trees in terms of rank functions that are versions of Cantor-Bendixson rank. We prove that automatic linear orders and automatic trees have finite rank. As an application we provide a procedure for deciding the isomorphism problem for automatic ordinals. We also investigate the complexity and definability of infinite paths in automatic trees. In particular, we show that every infinite path in an automatic tree with countably many infinite paths is a regular language.
S. Rubin, B. Khoussainov and F. Stephan, "On Automatic Partial Orders," Logic in Computer Science, Symposium on(LICS), Ottawa, Canada, 2003, pp. 168.