A Cantor dynamical system is slow if and only if all its finite orbits are attracting

If only we all cared.

Embedding If and Only If

Compounds of indicative conditionals present some puzzling phenomena. Perhaps most striking, some nested indicative conditionals are uninterpretable. Proponents of NTV hold that indicative conditionals do not have truth values, and they use this to explain why nested indicative conditionals are sometimes uninterpretable: the embedded conditional does not provide the truth conditions needed by t...

Markets are efficient if and only if P = NP

I prove that if markets are efficient, meaning current prices fully reflect all information available in past prices, then P = NP , meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can “program” the market to solve NP -complete problems. Since P probably does not equal NP , ma...

A Negative Conjunctive Query is Easy if and only if it is Beta-Acyclic

It is known that the data complexity of a Conjunctive Query (CQ) is determined only by the way its variables are shared between atoms, reflected by its hypergraph. In particular, Yannakakis [18, 3] proved that a CQ is decidable in linear time when it is α-acyclic, i.e. its hypergraph is α-acyclic; Bagan et al. [2] even state: Any CQ is decidable in linear time iff it is α-acyclic. (under certai...

Quadrangulations of the projective plane are t-perfect if and only if they are bipartite

We show that every non-bipartite quadrangulation of the projective plane contains an odd wheel as a t-minor and is thus t-imperfect.