TY - GEN

T1 - Testing computability by width two OBDDs

AU - Ron, Dana

AU - Tsur, Gilad

PY - 2009

Y1 - 2009

N2 - 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/∈. 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 Õ(log(n)/ ∈) queries.

AB - 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/∈. 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 Õ(log(n)/ ∈) queries.

UR - http://www.scopus.com/inward/record.url?scp=70350587314&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-03685-9_51

DO - 10.1007/978-3-642-03685-9_51

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AN - SCOPUS:70350587314

SN - 3642036848

SN - 9783642036842

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 686

EP - 699

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009

Y2 - 21 August 2009 through 23 August 2009

ER -