2026-07-31T14:21:13Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14503 2024-03-06T10:54:11Z ddc:004 open_access

The Simplest Non-Regular Deterministic Context-Free Language Jančar, Petr Šíma, Jiří deterministic context-free language truth-table reduction Mealy automaton pushdown automaton 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 ∈ {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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Petr Jančar and Jiří Šíma 2021 Is Part Of LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2021.63 urn:nbn:de:0030-drops-145037 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.63 eng https://creativecommons.org/licenses/by/4.0/legalcode