@inproceedings{ajtai1987monotone, author = {Ajtai, Miklos and Gurevich, Yuri}, title = {Monotone Versus Positive}, year = {1987}, month = {April}, abstract = {A number of famous theorems about first-order logic were disproved in [60] in the case of finite structures, but Lyndon's theorem on monotone vs. positive resisted the attack. It is defeated here. The counter-example gives a uniform sequence of constant-depth polynomial-size (functionally) monotone boolean circuits not equivalent to any (however nonuniform) sequence of constant-depth polynomial-size positive boolean circuits.}, url = {http://approjects.co.za/?big=en-us/research/publication/monotone-versus-positive/}, pages = {1004-1015}, journal = {Journal of ACM}, volume = {34}, }