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National Repository of Grey Literature 1 records found  Search took 0.01 seconds. 
Monotone functions avoiding majorities
 Petr, Jan ; Barto, Libor (advisor) ; Mottet, Antoine (referee)
In the past five years, the Promise Constraint Satisfaction Problem (PCSP) has been a popular topic in computational complexity, covering a wide range of computational problems. In this work, we begin by introducing the PCSP and then turn our atten- tion to the still open problem of the PCSP over 'monotone folded Boolean structures'. Brakensiek and Guruswami showed in 2016 that the PCSP is in P if all odd majorities are polymorphisms between structures under consideration. We focus on the situation in which some of the odd majorities are not among the polymorphisms. We present a technique for proving NP-completeness of PCSPs that uses the notion of heavy sets. Our approach succeeds in proving that the absence of the 3-majority makes the PCSP NP-complete. We then give a few partial results for the case of the absence of the 5-majority. We finish by determining the size of the smallest heavy set for a particular family of functions. 1
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