Abstract

We introduce the infix inclusion problem of two languages S and T that decides whether or not S is a subset of the set of all infixes of T. This problem is motivated by the need for identifying malicious computation patterns according to their semantics, which are often disguised with additional sub-patterns surrounding information. In other words, malicious patterns are embedded as an infix of the whole pattern. We examine the infix inclusion problem for the case where a source S and a target T are finite, regular or context-free languages. We prove that the problem is 1) co-NP-complete when one of the languages is finite, 2) PSPACE-complete when both S and T are regular, 3) EXPTIME-complete when S is context-free and T is regular, 4) undecidable when S is either regular or context-free and T is context-free and 5) undecidable when one of S and T is in a language class where the emptiness of its languages is undecidable, even if the other is finite. We, furthermore, explore the infix inclusion problem for visibly pushdown languages, a subclass of context-free languages.

中文翻译：

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论中缀包含问题的可判定性

摘要

我们引入了两种语言S和T的中缀包含问题，该问题决定S是否是T的所有中缀集合的子集。这个问题的动机是需要根据语义识别恶意计算模式，这些模式通常用围绕信息的附加子模式进行伪装。换句话说，恶意模式作为整个模式的中缀嵌入。我们检查源S和目标T是有限、常规或上下文无关语言的情况下的中缀包含问题。我们证明问题是 1）当其中一种语言是有限的时，是co-NP完全的；2）当S和T都是正则的时候， PSPACE 是完全的；3）当S是上下文无关的并且T是正则的时，是EXPTIME 完全的， 4) 当S是常规的或上下文无关且T是上下文无关时不可判定，以及 5) 当S和T之一处于其语言的空性不可判定的语言类中时不可判定，即使另一个是有限的。此外，我们还探讨了明显下推语言（上下文无关语言的子类）的中缀包含问题。