On the distributional complexity of disjointness
Theoretical Computer Science
Learning &mgr;-branching programs with queries
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
On learning bounded-width branching programs
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Communication complexity
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On learning width two branching programs
Information Processing Letters
Query learning of bounded-width OBDDs
Theoretical Computer Science - Special issue on algorithmic learning theory
Testing problems with sublearning sample complexity
Journal of Computer and System Sciences
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing Membership in Languages that Have Small Width Branching Programs
SIAM Journal on Computing
Testing Basic Boolean Formulae
SIAM Journal on Discrete Mathematics
On Learning Programs and Small Depth Circuits
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Learning Ordered Binary Decision Diagrams
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
Journal of Computer and System Sciences - Special issue on FOCS 2002
Testing Low-Degree Polynomials over Prime Fields
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Testing for Concise Representations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Testing Computability by Width Two OBDDs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
An efficient query learning algorithm for ordered binary decision diagrams
Information and Computation
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
On testing computability by small width OBDDs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Property Testing Lower Bounds via Communication Complexity
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Testing computability by width-2 OBDDs where the variable order is unknown
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
IEEE Transactions on Information Theory
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
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Property testing is concerned with deciding whether an object (e.g. a graph or a function) has a certain property or is ''far'' (for a prespecified distance measure) from every object with that property. In this work, we consider the property of being computable by a read-once width-2Ordered Binary Decision Diagram (OBDD), also known as a branching program, in two settings. In the first setting, the order of the variables is fixed and given to the algorithm, while in the second setting it is not fixed. That is, while in the first setting we should accept a function f if it is computable by a width-2 OBDD with a given order of the variables, in the second setting we should accept a function f if there exists an order of the variables according to which a width-2 OBDD can compute f. 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 by performing a number of queries that is independent of the number of variables,n (and is linear in 1/@e, where @e is the distance parameter). In contrast, we show that testing computability by width-2 OBDDs when the order of variables is fixed and known requires a number of queries that grows logarithmically with n (for a constant @e), and we provide an algorithm that performs O@?(logn/@e) queries. For the case where the order is not fixed, we show that there is no testing algorithm that performs a number of queries that is sublinear in n.