Recognizing Read-Once Functions from Depth-Three Formulas
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Consider the following decision problem: for a given monotone Boolean function f decide, whether f is read-once. For this problem, it is essential how the input function f is represented. Our contribution consists of the following two results. We show that we can test in polynomial-time whether a given expression C D computes a read-once function, provided that C is a read-once monotone CNF and D is a read-once monotone DNF and all the variables of C occur also in D (recall that due to Gurvich, the problem is coNP-complete when C is read-2). The second result states that this is a coNP-complete problem to decide whether the expression A D_n computes a read-once function, where D_n is as above and A is the -- depth-3 read-once monotone Boolean formula (so that the entire expression A D_n is depth-3 read-2). This result improves the result of elbassioni2011readability in the depth and the result of gurvich2010it in the readability of the input formula.
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