Abstract
The negation width of a Boolean AND, OR, NOT circuit computing a monotone Boolean function f is the minimum number w such that the unique formal DNF produced (purely syntactically) by the circuit contains each prime implicant of f extended by at most w solely negated variables. The negation width of monotone circuits is zero. We first show that already a moderate allowed negation width can substantially decrease the size of monotone circuits. Our main result is a general reduction: if a monotone Boolean function f can be computed by a non-monotone circuit of size s and negation width w, then f can be also computed by a monotone circuit of size s times 4min{wm,mw}logM, where m is the maximum length of a prime implicant and M is the total number of prime implicants of f.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
