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oai:drops-oai.dagstuhl.de:18615 2024-03-06T11:02:16Z ddc:004 open_access

On the Work of Dynamic Constant-Time Parallel Algorithms for Regular Tree Languages and Context-Free Languages Schmidt, Jonas Schwentick, Thomas Todtenhoefer, Jennifer Dynamic complexity work parallel constant time Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed with the goal to minimise work (or, equivalently, the number of processors). In fact, their inspection yields the work bounds 𝒪(n²) and 𝒪(n⁷) per change operation, respectively. In this paper, dynamic algorithms for regular tree languages are proposed that generalise the previous algorithms in that they allow unbounded node rank and leaf insertions, while improving the work bound from 𝒪(n²) to 𝒪(n^ε), for arbitrary ε > 0. For context-free languages, algorithms with better work bounds (compared with 𝒪(n⁷)) for restricted classes are proposed: for every ε > 0 there are such algorithms for deterministic context-free languages with work bound 𝒪(n^{3+ε}) and for visibly pushdown languages with work bound 𝒪(n^{2+ε}). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jonas Schmidt and Thomas Schwentick and Jennifer Todtenhoefer 2023 Is Part Of LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2023.81 urn:nbn:de:0030-drops-186152 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.81 eng https://creativecommons.org/licenses/by/4.0/legalcode