Weak states on posets are defined which are in some analogy to states on orthomodular posets used in axiomatic quantum mechanics. It is shown how certain properties of the set of weak states characterize certain properties of the underlying poset. Orthomodular posets serve as algebraic models for logics in axiomatic quantum mechanics. States on them are considered which reflect the properties o...

We prove, under a computational complexity hypothesis, that it is consistent with the true universal theory of p-time algorithms specific function extending $n$ bits to $m \geq n^2$ violates dual weak pigeonhole principle: every string $y$ length $m$ equals value for some $x$ $n$. The truth-table assigning circuit table computes and hypothesis language in P has circuits fixed polynomial size $n...