LIPIcs.MFCS.2023.81.pdf
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On the Work of Dynamic Constant-Time Parallel Algorithms for Regular Tree Languages and Context-Free Languages
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48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS) - License:
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- Publication Date: 2023-08-21
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Acknowledgements
We are grateful to Jens Keppeler and Christopher Spinrath for careful proof reading.
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Jonas Schmidt, Thomas Schwentick, and Jennifer Todtenhoefer. On the Work of Dynamic Constant-Time Parallel Algorithms for Regular Tree Languages and Context-Free Languages. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 81:1-81:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.MFCS.2023.81
Abstract
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}).
Subject Classification
ACM Subject Classification
- Theory of computation → Formal languages and automata theory
- Theory of computation → Parallel algorithms
Keywords
- Dynamic complexity
- work
- parallel constant time
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