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Balancing Straight-line Programs

Authors:

Markus LohreyAuthors Info & Claims

Journal of the ACM (JACM), Volume 68, Issue 4

Article No.: 27, Pages 1 - 40

https://doi.org/10.1145/3457389

Published: 30 June 2021 Publication History

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Abstract

We show that a context-free grammar of size

that produces a single string

of length

(such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for

of size

, whose unique derivation tree has depth

. This solves an open problem in the area of grammar-based compression, improves many results in this area, and greatly simplifies many existing constructions. Similar results are shown for two formalisms for grammar-based tree compression: top dags and forest straight-line programs. These balancing results can be all deduced from a single meta-theorem stating that the depth of an algebraic circuit over an algebra with a certain finite base property can be reduced to

with the cost of a constant multiplicative size increase. Here,

refers to the size of the unfolding (or unravelling) of the circuit. In particular, this results applies to standard arithmetic circuits over (noncommutative) semirings.

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Cited By

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https://dl.acm.org/doi/10.1007/s00236-025-00481-3
Shibata HIshihata MInenaga S(2025)Packed Acyclic Deterministic Finite AutomataSOFSEM 2025: Theory and Practice of Computer Science10.1007/978-3-031-82697-9_21(284-297)Online publication date: 21-Jan-2025
https://dl.acm.org/doi/10.1007/978-3-031-82697-9_21
Lohrey MSchmid M(2024)Enumeration for MSO-Queries on Compressed TreesProceedings of the ACM on Management of Data10.1145/36511412:2(1-17)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651141
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Index Terms

Balancing Straight-line Programs
1. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Data compression
  2. Formal languages and automata theory
    1. Grammars and context-free languages

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 68, Issue 4

August 2021

297 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3468065

Editor:
Éva Tardos
Cornell University, United States

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Copyright © 2021 Association for Computing Machinery.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 June 2021

Accepted: 01 March 2021

Revised: 01 February 2021

Received: 01 June 2020

Published in JACM Volume 68, Issue 4

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National Science Centre, Poland
DFG research project

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Cited By

Navarro GOlivares FUrbina C(2025)Generalized straight-line programsActa Informatica10.1007/s00236-025-00481-362:1Online publication date: 1-Mar-2025
https://dl.acm.org/doi/10.1007/s00236-025-00481-3
Shibata HIshihata MInenaga S(2025)Packed Acyclic Deterministic Finite AutomataSOFSEM 2025: Theory and Practice of Computer Science10.1007/978-3-031-82697-9_21(284-297)Online publication date: 21-Jan-2025
https://dl.acm.org/doi/10.1007/978-3-031-82697-9_21
Lohrey MSchmid M(2024)Enumeration for MSO-Queries on Compressed TreesProceedings of the ACM on Management of Data10.1145/36511412:2(1-17)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651141
Kempa DKociumaka T(2024)Lempel-Ziv (LZ77) Factorization in Sublinear Time2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00122(2045-2055)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00122
Goga ADepuydt LBrown NFostier JGagie TNavarro G(2024)Faster Maximal Exact Matches with Lazy LCP Evaluation2024 Data Compression Conference (DCC)10.1109/DCC58796.2024.00020(123-132)Online publication date: 19-Mar-2024
https://doi.org/10.1109/DCC58796.2024.00020
Cleary AWinjum JDood JInenaga S(2024)Revisiting the Folklore Algorithm for Random Access to Grammar-Compressed StringsString Processing and Information Retrieval10.1007/978-3-031-72200-4_7(88-101)Online publication date: 19-Sep-2024
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Carfagna LManzini GRomana GSciortino MUrbina C(2024)Generalization of Repetitiveness Measures for Two-Dimensional StringsString Processing and Information Retrieval10.1007/978-3-031-72200-4_5(57-72)Online publication date: 19-Sep-2024
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Takasaka AI T(2024)Space-Efficient SLP Encoding for O(log N)-Time Random AccessString Processing and Information Retrieval10.1007/978-3-031-72200-4_25(336-347)Online publication date: 19-Sep-2024
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Radoszewski JZuba W(2024)Computing String Covers in Sublinear TimeString Processing and Information Retrieval10.1007/978-3-031-72200-4_21(272-288)Online publication date: 23-Sep-2024
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Gagie T(2024)How to Find Long Maximal Exact Matches and Ignore Short OnesDevelopments in Language Theory10.1007/978-3-031-66159-4_10(131-140)Online publication date: 12-Aug-2024
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