Abstract
We investigate the problems of testing membership in the subset of the positive numbers produced at the output of 
combinational circuits. These problems are a natural modification of those studied by McKenzie and Wagner (2003), where circuits computed sets of natural numbers. It turns out that the missing 0 has strong implications, not only because 0 can be used to test for emptiness. We show that the membership problem for the general case and for 
is PSPACE-complete, whereas it is NEXPTIME-hard if one allows 0. Furthermore, testing membership for 
is NL-complete (as opposed to 
-hard), and several other cases are resolved.
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Breunig, HG. (2007). The Complexity of Membership Problems for Circuits over Sets of Positive Numbers. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_12
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DOI: https://doi.org/10.1007/978-3-540-74240-1_12
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