Abstract
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In this work, we design new algorithms for the threshold
- Amir Abboud, Arturs Backurs, and Virginia Vassilevska Williams. 2015. If the Current Clique Algorithms are Optimal, So is Valiant’s Parser. In FOCS 2015. 98–117. https://doi.org/10.1109/FOCS.2015.16Google ScholarDigital Library
- Alfred V. Aho and Thomas G. Peterson. 1972. A Minimum Distance Error-Correcting Parser for Context-Free Languages. SIAM J. Comput. 1, 4 (1972), 305–312. https://doi.org/10.1137/0201022Google ScholarDigital Library
- Josh Alman and Virginia Vassilevska Williams. 2021. A Refined Laser Method and Faster Matrix Multiplication. In SODA 2021. 522–539. https://doi.org/10.1137/1.9781611976465.32Google ScholarCross Ref
- Noga Alon, Zvi Galil, and Oded Margalit. 1997. On the Exponent of the All Pairs Shortest Path Problem. J. Comput. Syst. Sci. 54, 2 (1997), 255–262. https://doi.org/10.1006/jcss.1997.1388Google ScholarDigital Library
- Arturs Backurs and Krzysztof Onak. 2016. Fast Algorithms for Parsing Sequences of Parentheses with Few Errors. In PODS 2016. 477–488. https://doi.org/10.1145/2902251.2902304Google ScholarDigital Library
- Karl Bringmann, Fabrizio Grandoni, Barna Saha, and Virginia Vassilevska Williams. 2019. Truly Subcubic Algorithms for Language Edit Distance and RNA Folding via Fast Bounded-Difference Min-Plus Product. SIAM J. Comput. 48, 2 (2019), 481–512. https://doi.org/10.1137/17M112720XGoogle ScholarDigital Library
- Shucheng Chi, Ran Duan, and Tianle Xie. 2022. Faster Algorithms for Bounded-Difference Min-Plus Product. In SODA 2022. 1435–1447. https://doi.org/10.1137/1.9781611977073.60Google Scholar
- Shucheng Chi, Ran Duan, Tianle Xie, and Tianyi Zhang. 2022. Faster Min-plus Product for Monotone Instances. (2022), 1529–1542. https://doi.org/10.1145/3519935.3520057Google ScholarDigital Library
- Noam Chomsky and Marcel Paul Schützenberger. 1963. The Algebraic Theory of Context-Free Languages. Studies in Logic (1963). https://doi.org/10.1016/s0049-237x(08)72023-8Google Scholar
- Debarati Das, Tomasz Kociumaka, and Barna Saha. 2022. Improved Approximation Algorithms for Dyck Edit Distance and RNA Folding. In ICALP 2022, Vol. 229. 49:1–49:20. https://doi.org/10.4230/LIPIcs.ICALP.2022.49Google Scholar
- Mark de Berg, Otfried Cheong, Marc J. van Kreveld, and Mark H. Overmars. 2008. Computational geometry: algorithms and applications, 3rd Edition. Springer. https://www.worldcat.org/oclc/227584184Google ScholarCross Ref
- Anita Dürr. 2022. Improved Bounds for Rectangular Monotone Min-Plus Product. https://doi.org/10.48550/ARXIV.2208.02862Google Scholar
- Johannes Fischer and Volker Heun. 2006. Theoretical and Practical Improvements on the RMQ-Problem, with Applications to LCA and LCE. In Combinatorial Pattern Matching. 36–48. https://doi.org/10.1007/11780441_5Google ScholarDigital Library
- Francois Le Gall and Florent Urrutia. 2018. Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor. In SODA 2018. 1029–1046. https://doi.org/10.1137/1.9781611975031.67Google ScholarCross Ref
- Robin R. Gutell, Jamie Cannone, Zhidi Shang, Yushi Du, and Martin J. Serra. 2000. A story: unpaired adenosine bases in ribosomal RNAs. Journal of Molecular Biology 304, 3 (2000), 335–354. https://doi.org/10.1006/jmbi.2000.4172Google ScholarCross Ref
- Michael A. Harrison. 1978. Introduction to Formal Language Theory. Addison-Wesley Longman Publishing Co., Boston, MA, USA, 1st edition.Google Scholar
- Rajesh Jayaram and Barna Saha. 2017. Approximating Language Edit Distance Beyond Fast Matrix Multiplication: Ultralinear Grammars Are Where Parsing Becomes Hard!. In ICALP 2017(Leibniz International Proceedings in Informatics (LIPIcs), Vol. 80). 19:1–19:15. https://doi.org/10.4230/LIPIcs.ICALP.2017.19Google Scholar
- Dexter C. Kozen. 1997. Automata and Computability(1st ed.). Springer-Verlag, Berlin, Heidelberg.Google Scholar
- Andreas Krebs, Nutan Limaye, and Srikanth Srinivasan. 2011. Streaming Algorithms for Recognizing Nearly Well-Parenthesized Expressions. In MFCS 2011. 412–423. https://doi.org/10.1007/978-3-642-22993-0_38Google Scholar
- Gad M. Landau, Eugene W. Myers, and Jeanette P. Schmidt. 1998. Incremental String Comparison. SIAM J. Comput. 27, 2 (1998), 557–582. https://doi.org/10.1137/S0097539794264810Google ScholarCross Ref
- Gad M. Landau and Uzi Vishkin. 1988. Fast String Matching with k Differences. J. Comput. System Sci. 37, 1 (1988), 63–78. https://doi.org/10.1016/0022-0000(88)90045-1Google ScholarDigital Library
- Lillian Lee. 2002. Fast Context-Free Grammar Parsing Requires Fast Boolean Matrix Multiplication. J. ACM 49, 1 (Jan. 2002), 1–15. https://doi.org/10.1145/505241.505242Google ScholarDigital Library
- J. Ian Munro and Venkatesh Raman. 2001. Succinct Representation of Balanced Parentheses and Static Trees. SIAM J. Comput. 31, 3 (2001), 762–776. https://doi.org/10.1137/S0097539799364092Google ScholarDigital Library
- Gene Myers. 1995. Approximately matching context-free languages. Inform. Process. Lett. 54, 2 (1995), 85–92. https://doi.org/10.1016/0020-0190(95)00007-yGoogle ScholarDigital Library
- Alexander Okhotin. 2014. Parsing by matrix multiplication generalized to Boolean grammars. Theoretical Computer Science 516 (2014), 101–120. https://doi.org/10.1016/j.tcs.2013.09.011Google ScholarDigital Library
- Sanguthevar Rajasekaran, Sahar Al Seesi, and Reda Ammar. 2009. Improved Algorithms for Parsing ESLTAGs: A Grammatical Model Suitable for RNA Pseudoknots. In Bioinformatics Research and Applications. 135–147. https://doi.org/10.1007/978-3-642-01551-9_14Google ScholarDigital Library
- Barna Saha. 2014. The Dyck Language Edit Distance Problem in Near-Linear Time. In FOCS 2014. 611–620. https://doi.org/10.1109/FOCS.2014.71Google ScholarDigital Library
- Barna Saha. 2015. Language Edit Distance and Maximum Likelihood Parsing of Stochastic Grammars: Faster Algorithms and Connection to Fundamental Graph Problems. In FOCS 2015. 118–135. https://doi.org/10.1109/FOCS.2015.17Google ScholarDigital Library
- Barna Saha. 2017. Fast Space-Efficient Approximations of Language Edit Distance and RNA Folding: An Amnesic Dynamic Programming Approach. In FOCS 2017. 295–306. https://doi.org/10.1109/FOCS.2017.35Google Scholar
- Leslie G. Valiant. 1975. General Context-Free Recognition in Less than Cubic Time. J. Comput. Syst. Sci. 10, 2 (1975), 308–315. https://doi.org/10.1016/S0022-0000(75)80046-8Google ScholarDigital Library
- Virginia Vassilevska Williams and Yinzhan Xu. 2020. Truly Subcubic Min-Plus Product for Less Structured Matrices, with Applications. In SODA 2020. SIAM, 12–29. https://doi.org/10.1137/1.9781611975994.2Google ScholarCross Ref
Index Terms
- An Improved Algorithm for The k-Dyck Edit Distance Problem
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