Algorithms and Complexity

Volume 6078 of the series Lecture Notes in Computer Science pp 131-142

Testing Computability by Width-2 OBDDs Where the Variable Order is Unknown

  • Dana RonAffiliated withSchool of Electrical Engineering, Tel Aviv University
  • , Gilad TsurAffiliated withSchool of Electrical Engineering, Tel Aviv University

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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 design and analyze an algorithm 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 not known to us. That is, we must accept a function f if there exists an order of the variables according to which a width-2 OBDD can compute f. The query complexity of our algorithm is \(\tilde{O}({\rm log n}){\rm poly}(1/\epsilon)\). In previous work (in Proceedings of RANDOM, 2009) we designed an algorithm for testing computability by an OBDD with a fixed order, which is known to the algorithm. Thus, we extend our knowledge concerning testing of functions that are characterized by their computability using simple computation devices and in the process gain some insight concerning these devices.