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Testing Computability by Width Two OBDDs

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2009, RANDOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5687))

Abstract

Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is “far” (for some definition of far) from every object with that property. In this paper we give lower and upper bounds for testing functions for the property of being computable by a read-once width-2 Ordered Binary Decision Diagram (OBDD), also known as a branching program, where the order of the variables is known. Width-2 OBDDs generalize two classes of functions that have been studied in the context of property testing - linear functions (over GF(2)) and monomials. In both these cases membership can be tested in time that is linear in 1/ε. Interestingly, unlike either of these classes, in which the query complexity of the testing algorithm does not depend on the number, n, of variables in the tested function, we show that (one-sided error) testing for computability by a width-2 OBDD requires Ω(log(n)) queries, and give an algorithm (with one-sided error) that tests for this property and performs \(\tilde{O}(\log(n)/\epsilon)\) queries.

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Author information

Authors and Affiliations

  1. School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel

    Dana Ron & Gilad Tsur

Authors
  1. Dana Ron
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  2. Gilad Tsur
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Editor information

Editors and Affiliations

  1. Dept. of Applied Math and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Irit Dinur

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Technion, Computer Science Department, 32000, Haifa, Israel

    Joseph Naor

  4. University of Geneva, Centre Universitaire d’Informatique, Battelle Bat. A, 7 rte de Drize, 1227, Carouge, Switzerland

    José Rolim

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© 2009 Springer-Verlag Berlin Heidelberg

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Ron, D., Tsur, G. (2009). Testing Computability by Width Two OBDDs. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_51

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  • DOI: https://doi.org/10.1007/978-3-642-03685-9_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03684-2

  • Online ISBN: 978-3-642-03685-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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