Word Problems on Compressed Words

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


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.


Polynomial Time Word Problem Membership Problem Polynomial Time Hierarchy Thue System 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Markus Lohrey
    • 1
  1. 1.Universität Stuttgart, FMIStuttgartGermany

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