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The Simplest Non-Regular Deterministic Context-Free Language
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SYSNO ASEP 0543570 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title The Simplest Non-Regular Deterministic Context-Free Language Author(s) Jančar, P. (CZ)
Šíma, Jiří (UIVT-O) RID, SAI, ORCIDNumber of authors 2 Article number 63 Source Title 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). - Dagstuhl : Dagstuhl Publishing, 2021 / Bonchi F. ; Puglisi S. J. - ISSN 1868-8969 Number of pages 18 s. Publication form Online - E Action MFCS 2021: International Symposium on Mathematical Foundations of Computer Science /46./ Event date 23.08.2021 - 27.08.2021 VEvent location Tallinn Country EE - Estonia Event type WRD Language eng - English Country DE - Germany Keywords deterministic context-free language ; truth-table reduction ; Mealy automaton ; pushdown automaton Subject RIV IN - Informatics, Computer Science OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) R&D Projects GA19-05704S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 EID SCOPUS 85115356156 DOI 10.4230/LIPIcs.MFCS.2021.63 Annotation We introduce a new notion of C-simple problems for a class C of decision problems (i.e. languages), w.r.t. a particular reduction. A problem is C-simple if it can be reduced to each problem in C. This can be viewed as a conceptual counterpart to C-hard problems to which all problems in C 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 in {a,b}^*} is not DCFL'-simple. By describing an application in the area of neural networks (elaborated in another paper), we demonstrate that C-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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2022
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