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The Complexity of Problems on Implicitly Represented Inputs

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SOFSEM 2006: Theory and Practice of Computer Science (SOFSEM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3831))

Abstract

Highly regular data can be represented succinctly by various kinds of implicit data structures. Many problems in P are known to be hard if their input is given as circuit or Ordered Binary Decision Diagram (OBDD). Nevertheless, in practical areas like CAD and Model Checking, symbolic algorithms using functional operations on OBDD-represented data are well-established. Their theoretical analysis has mostly been restricted to the number of functional operations yet. We show that P-complete problems have no symbolic algorithms using a polylogarithmic number of functional operations, unless P=NC. Moreover, we complement PSPACE-hardness results for problems on OBDD-represented inputs by fixed-parameter intractability results, where the OBDD width serves as the fixed parameter.

Extended version available at http://ls2-www.cs.uni-dortmund.de/s̃awitzki/.

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Author information

Authors and Affiliations

  1. Computer Science 2, University of Dortmund, D-44221, Dortmund, Germany

    Daniel Sawitzki

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  1. Daniel Sawitzki
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Editors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jiří Wiedermann  & Július Štuller  & 

  2. Department of Information and Computer Sciences, University of Utrecht, P.O. Box 80.089, 3508, Utrecht, TB, The Netherlands

    Gerard Tel

  3. Faculty of Mathematics and Physics, Charles University, Prague

    Jaroslav Pokorný

  4. Institute of Informatics and Software Engineering Faculty of Informatics and Information technologies, Slovak University of Technology, Ilkovičova 3, 842 16, Bratislava

    Mária Bieliková

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Sawitzki, D. (2006). The Complexity of Problems on Implicitly Represented Inputs. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_45

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  • DOI: https://doi.org/10.1007/11611257_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31198-0

  • Online ISBN: 978-3-540-32217-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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