Testing computability by width-two OBDDs

Ron, Dana; Tsur, Gilad

doi:10.1016/j.tcs.2011.11.007

Cited by 7 publications

(13 citation statements)

References 25 publications

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“…Tackling this case was posed as an open question in [28]. Our technique is able to handle this case as well, as shown in our second main result.…”

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confidence: 64%

“…The problem of testing whether a function f is computable by an OBDD was first studied by Ron and Tsur in [25]. They point out that although previous testing results have looked at the problem of testing whether f has a simple form, it seems reasonable instead to fix a simple model of computation, and test whether f is computable within the model.…”

Section: Results For Width-2 and Width-3 Obddsmentioning

confidence: 99%

“…In subsequent work [28], the same authors gave a different proof which improved the bound to Ω(n) for nonadaptive testers, even with two-sided error, thus achieving the same bound as in Theorem 1. The "no" instances (functions that are far from width-2 OBDDs) we use in our proof are partially inspired by [28]. However, our proof technique uses a different, more modular approach, as we shall discuss below.…”

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confidence: 90%

“…For the first variant of the width-2 OBDD testing problem, where the variables must occur in a fixed order, Ron and Tsur gave an adaptive upper bound ofÕ(log n)·poly(1/ ) queries [25] (here theÕ notation hides factors of log log n). This is an exponential improvement over the Ω(n) queries required for learning the same class.…”

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confidence: 99%

“…In [25], Ron and Tsur gave a lower bound of Ω(log n) for testing fixed-order width-2 OBDDs with one-sided error. However, this proof was recently found to contain a flaw, which we discuss in Appendix B.…”

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confidence: 99%

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Lower Bounds for Testing Computability by Small Width OBDDs

Brody

Matulef

2011

Lecture Notes in Computer Science

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Abstract. We consider the problem of testing whether a function f : {0, 1} n → {0, 1} is computable by a read-once, width-2 ordered binary decision diagram (OBDD), also known as a branching program. This problem has two variants: one where the variables must occur in a fixed, known order, and one where the variables are allowed to occur in an arbitrary order. We show that for both variants, any nonadaptive testing algorithm must make Ω(n) queries, and thus any adaptive testing algorithm must make Ω(log n) queries.We also consider the more general problem of testing computability by width-w OBDDs where the variables occur in a fixed order. We show that for any constant w ≥ 4, Ω(n) queries are required, resolving a conjecture of Goldreich [15].We prove all of our lower bounds using a new technique of Blais, Brody, and Matulef [6], giving simple reductions from known hard problems in communication complexity to the testing problems at hand. Our result for width-2 OBDDs provides the first example of the power of this technique for proving strong nonadaptive bounds.

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“…Tackling this case was posed as an open question in [28]. Our technique is able to handle this case as well, as shown in our second main result.…”

mentioning

confidence: 64%

Section: Results For Width-2 and Width-3 Obddsmentioning

confidence: 99%

mentioning

confidence: 90%

mentioning

confidence: 99%

mentioning

confidence: 99%