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On the computing powers of L-reductions of insertion languages
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-11-19 , DOI: 10.1016/j.tcs.2020.11.029
Fumiya Okubo , Takashi Yokomori

We investigate the computing power of the following language operation %: Given two languages L1 over Σ and L2 over Γ with ΓΣ, we consider the language operation L1%L2={u0u1un|u=u0v1u1vnunL1 and viL2(1in)}. In this case we say that L(=L1%L2) is the L2-reduction of L1. This is extended to the language families as follows: L1%L2={L1%L2|L1L1,L2L2}. Among many works concerning Dyck-reductions, for the family of recursively enumerable languages RE, it was shown that LIN%{EQ}=RE (Jantzen & Petersen, 1994) with EQ={xnxn|nN} and that min-LIN%{D2}=RE (Hirose & Okawa, 1996, and Latteux & Turakainen, 1990), where LIN and min-LIN are the families of linear and minimal linear context-free languages, respectively.

In this paper, we show that each recursively enumerable language L can be represented in the form L=K%D, for some KINS30 and a Dyck language D, where INS0 (INS30) denotes the family of insertion languages (insertion languages where the maximum length of the string to be inserted is 3). We can refine it as INS0%{D2}=RE, where D2 denotes the Dyck language over binary alphabet. For context-free languages, we show that INS30%F=CF, where F is the family of finite sets. This also derives that INS0%{MIR}=CF with MIR={xxR|x{0,1}}. Further, for regular languages, it is shown that each regular language R can be represented in the form R=K%F, for some KINS20 and a finite set F={abba|aV}. We also present some results which characterize the computability and properties of L in the framework of L2-reduction of L1.

It is intriguing to note that, from the DNA computing point of view, the notion of L-reduction is naturally motivated by a molecular biological functioning well-known as DNA(RNA) splicing occurring in most eukaryotic genes.



中文翻译:

关于...的计算能力 大号-减少插入语言

我们研究以下语言操作%的计算能力:给定两种语言 大号1个 超过Σ和 大号2个 在Γ上 ΓΣ,我们考虑语言操作 大号1个大号2个={ü0ü1个üñ|ü=ü0v1个ü1个vñüñ大号1个 和 v一世大号2个1个一世ñ}。在这种情况下,我们说大号=大号1个大号2个 是个 大号2个-减少 大号1个。这扩展到语言族,如下所示:大号1个大号2个={大号1个大号2个|大号1个大号1个大号2个大号2个}。在众多关于Dyck归约的著作中,针对递归可枚举语言家族回覆,结果表明 {情商}=回覆 (Jantzen&Petersen,1994)与 情商={XñXñ|ññ}分钟-{d2个}=回覆 (Hirose和Okawa,1996年; Latteux和Turakainen,1990年),其中 和分钟 分别是线性和最小线性上下文无关语言的族。

在本文中,我们证明了每种递归可枚举语言L都可以用以下形式表示:大号=ķd, 对于一些 ķ惯导30和戴克语言D,其中惯导0惯导30)表示插入语言的族(插入语言,其中要插入的字符串的最大长度为3)。我们可以将其细化为惯导0{d2个}=回覆, 在哪里 d2个用二进制字母表示戴克语言。对于无上下文语言,我们表明惯导30F=碳纤维, 在哪里 F是有限集的族。这也得出惯导0{MIR}=碳纤维MIR={XX[R|X{01个}}。此外,对于常规语言,示出了每种常规语言R可以以以下形式表示:[R=ķF, 对于一些 ķ惯导2个0 和一个有限集 F={一种bb一种|一种伏特}。我们还提出了一些表征可计算性和特性的结果大号 在...的框架内 大号2个-减少 大号1个

有趣的是,从DNA计算的角度来看,L-还原的概念是由大多数真核基因中发生的众所周知的分子生物学功能即DNA(RNA)剪接自然激发的。

更新日期:2020-11-19
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