Isomorphism of regular trees and words

The complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are represented by NFAs (DFAs), the isomorphism problem for regular trees turns out to be EXPTIME-complete (resp. P-complete). In case the input automata are acyclic NFAs (acyclic DFAs), the corresponding trees are (succinctly represented) finite trees, and the isomorphism problem turns out to be PSPACE-complete (resp. Pcomplete). A linear order is regular if it is isomorphic to the lexicographic order on a regular language. A polynomial time algorithm for the isomorphism problem for regular linear orders (and even regular words, which generalize the latter) given by DFAs is presented. This solves an open problem by ´Esik and Bloom. A long version of this paper can be found in [18].

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Markus Lohrey, Christian Mathissen
• Keywords: CORR 2011, Education, Isomorphism Problem, Regular, Regular Language