文章基本信息

标题：The Simplest Non-Regular Deterministic Context-Free Language
本地全文：下载
作者：Jančar, Petr ; Šíma, Jiří
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2021
卷号：202
DOI：10.4230/LIPIcs.MFCS.2021.63
语种：English
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We introduce a new notion of ??-simple problems for a class ?? of decision problems (i.e. languages), w.r.t. a particular reduction. A problem is ??-simple if it can be reduced to each problem in ??. This can be viewed as a conceptual counterpart to ??-hard problems to which all problems in ?? reduce. Our concrete example is the class of non-regular deterministic context-free languages (DCFL'), with a truth-table reduction by Mealy machines. The main technical result is a proof that the DCFL' language L_# = {0^n1^n ∣ n ≥ 1} is DCFL'-simple, and can be thus viewed as one of the simplest languages in the class DCFL', in a precise sense. The notion of DCFL'-simple languages is nontrivial: e.g., the language L_R = {wcw^R∣ w ∈ {a,b}^*} is not DCFL'-simple.By describing an application in the area of neural networks (elaborated in another paper), we demonstrate that ??-simple problems under suitable reductions can provide a tool for expanding the lower-bound results known for single problems to the whole classes of problems.
关键词：deterministic context-free language;truth-table reduction;Mealy automaton;pushdown automaton