Approximating the distance to monotonicity of Boolean functions

Abstract We design a nonadaptive algorithm that, given oracle access to function which is ‐far from monotone, makes poly queries and returns an estimate with high probability, ‐approximation the distance of monotonicity. The analysis our relies on improvement directed isoperimetric inequality Khot, Minzer, Safra ( SIAM J. Comput. , 2018). Furthermore, we rule out ‐query that approximates monotonicity significantly better by showing for all constant every this problem requires queries. This answers question Seshadhri Property Testing Review 2014) case algorithms. obtain lower bound proving analogous erasure‐resilient (and tolerant) testers. Our method also yields same bounds unateness being ‐junta.