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Forbidding Sets and Normal Forms for Language Forbidding-Enforcing Systems

机译：语言禁止执行系统的禁止集和范式

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This paper investigates ways to reduce redundancy in forbidding sets for language forbidding-enforcing systems. A language forbidding set disallows combinations of subwords in a word, while permitting the presence of some parts of these combinations. Since a forbidding set is a potentially infinite set of finite sets of words, finding normal forms for forbidding sets is interesting from a combinatorics on words perspective and important for the theoretical investigation of language fe-systems, the connection between variants of fe-systems, and their applications to molecular computation. This paper shows that the minimal normal forms for forbidding sets defining classes of languages (fe-families) are also normal forms for forbidding sets defining single languages (fe-languages), but not necessarily minimal. Thus, an investigation of minimality and sufficient conditions for fe-languages are presented and it is shown that in special cases they coincide with a minimal normal form for fe-families.
机译：本文研究了减少语言禁止执行系统的禁止集中的冗余的方法。一种禁止语言的集合不允许单词中子词的组合，同时允许存在这些组合的某些部分。由于禁止集是单词的有限集的潜在无限集，因此从单词组合的角度出发，找到禁止集的范式很有趣，并且对于语言fe系统的理论研究，fe系统变体之间的联系，及其在分子计算中的应用。本文显示，用于定义语言类别（fe-families）的禁止集的最小范式也是用于定义单个语言（fe-languages）的禁止集的范式，但不一定是最小。因此，提出了对非母语的最低限度和充分条件的研究，结果表明，在特殊情况下，它们与非正规的正常形式相吻合。

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