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# The Simplest Non-Regular Deterministic Context-Free Language

- 1.0543570 - 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.

**Permanent Link:**http://hdl.handle.net/11104/0320756

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