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Word Problems on Compressed Words

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Automata, Languages and Programming (ICALP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3142))

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Abstract

We consider a compressed form of the word problem for finitely presented monoids, where the input consists of two compressed representations of words over the generators of a monoid \(\mathcal M\), and we ask whether these two words represent the same monoid element of \(\mathcal M\). For compression we use straight-line programs. For several classes of monoids we obtain completeness results for complexity classes in the range from P to EXPSPACE. As a by-product of our results on compressed word problems we obtain a fixed deterministic context-free language with a PSPACE-complete membership problem. The existence of such a language was open so far. Finally, we investigate the complexity of the compressed membership problem for various circuit complexity classes.

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Author information

Authors and Affiliations

  1. Universität Stuttgart, FMI, Universitätsstr. 38, 70569, Stuttgart, Germany

    Markus Lohrey

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  1. Markus Lohrey
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. Department of Mathematics, University of Turku, Turku, Finland

    Arto Lepistö

  4. Laboratory for Foundations of Computer Science, University of Edinburgh,  

    Donald Sannella

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Lohrey, M. (2004). Word Problems on Compressed Words. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_76

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  • DOI: https://doi.org/10.1007/978-3-540-27836-8_76

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

  • eBook Packages: Springer Book Archive

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