Functions that have read-once branching programs of quadratic size are not necessarily testable

Authors:
Beate Bollig;Ingo Wegener
Affiliations:
FB Informatik, LS 2, Universität Dortmund, 44221 Dortmund, Germany;FB Informatik, LS 2, Universität Dortmund, 44221 Dortmund, Germany
Venue:
Information Processing Letters
Year:
2003

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Abstract

A property of binary strings is constructed that has a representation by a collection of read-once branching programs of quadratic size but which is not ε-testable for some fixed ε 0. This shows that Newman's result [Proc. 41st FOCS, 2000, pp. 251-258]. cannot be generalized to functions representable by read-once branching programs of polynomial size.