字母表大小为4的比劳猜想

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Information and Computation Pub Date : 2025-08-20 DOI:10.1016/j.ic.2025.105342

Szymon Łopaciuk , Daniel Reidenbach

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引用次数: 0

摘要

1993年首次提出的比劳猜想是一个关于有限词及其后继词的基本问题，即通过删除单个字母的投影得到的词。该猜想指出，每一个词形原词，即不是任何非同一性词形的不动点的词，至少有一个词形原继承人。到目前为止，这个猜想的正确性已经在一些特殊情况下得到了证实，这些情况主要限制了字母表的大小。本文给出了下一种情况的证明，即对于字母大小为4的情况。

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The Billaud Conjecture for alphabet size 4

The Billaud Conjecture, first stated in 1993, is a fundamental problem on finite words and their heirs, i.e., the words obtained by a projection deleting a single letter. The conjecture states that every morphically primitive word, i.e., a word that is not a fixed point of any non-identity morphism, has at least one morphically primitive heir. The correctness of the conjecture has so far been established in a few special cases, which mainly restrict the alphabet size. In this paper we give a proof for the next such case, i.e., for alphabet size 4.

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来源期刊

Information and Computation 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

119

审稿时长

140 days

期刊介绍： Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as -Biological computation and computational biology- Computational complexity- Computer theorem-proving- Concurrency and distributed process theory- Cryptographic theory- Data base theory- Decision problems in logic- Design and analysis of algorithms- Discrete optimization and mathematical programming- Inductive inference and learning theory- Logic & constraint programming- Program verification & model checking- Probabilistic & Quantum computation- Semantics of programming languages- Symbolic computation, lambda calculus, and rewriting systems- Types and typechecking