# Tag Info

17

TL;DR. The metamathematics of binding are subtle: they seem trivial but aren't — whether you deal with (higher-order) logics or 𝜆-calculus. They're so subtle that binding representations form an open research field, with a competition (the POPLmark challenge) some years ago. There are even jokes by people in the field about the complexity of approaches to ...

5

On Closure Properties of #P in the Context of PF ∘ #P Note that FP and PF are the same complexity class. It is stated in proposition 2.1 on page 3 that FP ∘ #P = FP $^{\# P{ [1]}}$

4

There is an article from Alan Selman: A taxonomy of complexity classes of functions Please note, that i found this reference in an Answer (by Joshua Grochow) for this Question: Complexity class when reducing decision problem to function problem Note also the Comments from Kaveh: If you have a function you can look at the bit graph of the function which ...

2

I already answered how to construct such terms in a related question, so let me just amend that answer with some equations. A standard type constructor which has constructors and eliminators, for instance $A \times B$ has pairing and projections, will have: $\beta$-rules which says how destructors operate on constructors, for instance: $\pi_1 (a,b) \equiv ... 1 Consider the function$f(x, y) = 1 - e^{-(x + y)}$. Now$f(0, 0) = 0$,$f$is increasing and concave, since$g(t) = -e^{-t}$is concave. But$f(1, 0) + f(0, 1) = 2(1 - e^{-1}) > 1 - e^{-2} = f(1, 1)$, hence the claim doesn't hold even when$n = 2$. The claim doesn't hold for convex functions either.$f(x, y) = 2(x + y) + |x - y|$is one counterexample:$...

1

Let $n=1$. Let $\mu$ be the usual Lebesgue length measure on $[1/2,1]$, and let $\mu$ be the negative of the usual Lebesgue length measure on $[0,1/2]$. In particular, Lebesgue measure is $|\mu|$. Let $\mathcal U\subseteq [0,1]$ be a set of Lebesgue measure 0. (For instance, $\mathcal U$ could be the set of all numbers whose binary expansion does not ...

Only top voted, non community-wiki answers of a minimum length are eligible