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- W2078146321 abstract "We present another generalization of Higman's result ([2]) that the subsequence embedding relationship on a finitely generated free monoid is a well quasi order. Our result is analogous to the generalization of Higman's result given in [1] in the following manner. In the quasi orders we consider, we are given a finite set S of non-null words from Σ∗ and we demand that x1…xk+1 is less than or equal to x1a1…xkakxk+1 for any words x1,…,xk+1ϵΣ∗ and any single word a1…ak ϵ S, where aiϵΣ, 1⩽i⩽k. The least quasi order obtained in this fashion is denoted ⪅s. In contrast to the notion of subword unavoidability used in [1], S is said to be subsequence unavoidable (in Σ∗) if and only if there exists a k0 such that any word longer than k0 has a (nonempty) subsequence of letters (not necessarily contiguous) which form a word in S. We show that ⪅s is a well quasi order on Σ∗ if and only if S is subsequence unavoidable in Σ∗. As an application of this result, we show that the iterated shuffle ([1], [7], [8]) of a finite set S with itself is a regular language if and only if S is subsequence unavoidable." @default.
- W2078146321 created "2016-06-24" @default.
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- W2078146321 date "1985-12-01" @default.
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- W2078146321 title "Another generalization of Higman's well quasi order result on Σ∗" @default.
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- W2078146321 doi "https://doi.org/10.1016/0012-365x(85)90176-1" @default.
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