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A Sufficient Condition for Sets Hitting the Class of Read-Once Branching Programs of Width 3

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SOFSEM 2012: Theory and Practice of Computer Science (SOFSEM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7147))

Abstract

We characterize the hitting sets for read-once branching programs of width 3 by a so-called richness condition which is independent of a rather technical definition of branching programs. The richness property proves to be (in certain sense) necessary and sufficient condition for such hitting sets. In particular, we show that any rich set extended with all strings within Hamming distance of 3 is a hitting set for width-3 read-once branching programs. Applying this result to an example of an efficiently constructible rich set from our previous work we achieve an explicit polynomial time construction of an ε-hitting set for read-once branching programs of width 3 with acceptance probability ε > 11/12.

This research was partially supported by projects GA ČR P202/10/1333, MŠMT ČR 1M0545, and AV0Z10300504.

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Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, P. O. Box 5, 18207, Prague 8, Czech Republic

    Jiří Šíma & Stanislav Žák

Authors
  1. Jiří Šíma
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  2. Stanislav Žák
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Editors and Affiliations

  1. Faculty of Informatics and Information Technologies, Institute of Informatics and Software Engineering, Slovak University of Technology in Bratislava, Ilkovičova 3, 842 16, Bratislava 4, Slovakia

    Mária Bieliková

  2. Dept. of Intelligent Systems and Business Informatics, Alpen-Adria-Universität Klagenfurt, Universitätsstr. 65-57, 9020, Klagenfurt, Austria

    Gerhard Friedrich

  3. Department of Computer Science, University of Oxford, UK

    Georg Gottlob

  4. Security Engineering Group, Technische Universität Darmstadt, Hochschulstr. 10, 64289, Darmstadt, Germany

    Stefan Katzenbeisser

  5. University of Illinois at Chicago, Dept. of Math., Stat. and Comp. Sci, 851 S. Morgan Street, Chicago, IL 60607-7045, USA; and University of Szeged, Research Group on Artificial Intelligence of the Hungarian Academy of Sciences, 6701 Szeged, Postafiók, Hungary

    György Turán

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Šíma, J., Žák, S. (2012). A Sufficient Condition for Sets Hitting the Class of Read-Once Branching Programs of Width 3. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds) SOFSEM 2012: Theory and Practice of Computer Science. SOFSEM 2012. Lecture Notes in Computer Science, vol 7147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27660-6_33

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  • DOI: https://doi.org/10.1007/978-3-642-27660-6_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27659-0

  • Online ISBN: 978-3-642-27660-6

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