The equational theory of regular words

On the Order Type of Scattered Context-Free Orderings

“…in which each nonterminal generates a prefix-free language) is computable, thus the isomorphism problem of context-free ordinals is decidable if the ordinals in question are given as the lexicograpic ordering of prefix grammars. Also, the isomorphism problem of regular orderings is decidable as well [15,3]. At the other hand, it is undecidable for a context-free grammar whether it generates a dense language, hence the isomorphism problem of context-free orderings in general is undecidable [7].…”

Isomorphisms of scattered automatic linear orders

“…Thomas proved that the isomorphism problem for these words is decidable [29], the complexity of this problem was determined by Lohrey and Mathissen [24]. Based on techniques and results from [2], we will show that, given a regular language L, it is decidable whether (L; ≤ lex ) is rigid. This proof requires the consideration of regular words: An extended word is a labeled linear order with a finite set of labels.…”

The Order Type of Scattered Context-Free Orderings of Rank One Is Computable

“…If each Q x has the same order type o 1 and Q has order type o 2 , then the above sum has order type o 1 × o 2 . If Q = [2], then the sum is usally written as Q 1 + Q 2 .…”