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The Simplest Non-Regular Deterministic Context-Free Language

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    0543570 - ÚI 2022 RIV DE eng C - Conference Paper (international conference)
    Jančar, P. - Šíma, Jiří
    The Simplest Non-Regular Deterministic Context-Free Language.
    46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Dagstuhl: Dagstuhl Publishing, 2021 - (Bonchi, F.; Puglisi, S.), č. článku 63. LIPIcs - Leibniz International Proceedings in Informatics, 202. ISSN 1868-8969.
    [MFCS 2021: International Symposium on Mathematical Foundations of Computer Science /46./. Tallinn (EE), 23.08.2021-27.08.2021]
    R&D Projects: GA ČR(CZ) GA19-05704S
    Institutional support: RVO:67985807
    Keywords : deterministic context-free language * truth-table reduction * Mealy automaton * pushdown automaton
    OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

    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.
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    0543570-aoa.pdf81 MBOA CC BY 4.0Publisher’s postprintopen-access
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