We explain an asymmetric Prover-Delayer game which precisely characterizes proof size in treelike Resolution. This game was previously described in a parameterized complexity context to show lower bounds for parameterized formulas [BGL11] and for the classical pigeonhole principle [BGL10]. The main point of this note is to show that the asymmetric game in fact characterizes tree-like Resolution...

We explain an asymmetric Prover-Delayer game which precisely characterizes proof size in tree-like Resolution. This game was previously described in a parameterized complexity context to show lower bounds for parameterized formulas [BGL13] and for the classical pigeonhole principle [BGL10]. The main point of this note is to show that the asymmetric game in fact characterizes tree-like Resolutio...

We investigate the proof complexity of analytic subsystems of the deep inference proof system SKSg (the calculus of structures). Exploiting the fact that the so-called cut rule of SKSg does not correspond to cut in the sequent calculus, but to the ¬-left rule, we establish that the “analytic” system KSg + c↑ has essentially the same complexity as the monotone Gentzen calculus MLK . In particula...

In combinatorics, Ramsey Theory considers partitions of some mathematical objects and asks the following question: how large must the original object be in order to guarantee that at least one of the parts in the partition exhibits some property? Perhaps the most familiar case is the well-known Pigeonhole Principle: if m pigeonholes house p pigeons where p m, then one of the pigeonholes must co...

In this note we show that the asymmetric Prover-Delayer game developed in (ECCC, TR10–059) for Parameterized Resolution is also applicable to other treelike proof systems. In particular, we use this asymmetric Prover-Delayer to show a lower bound of the form 2Ω(n logn) for the pigeonhole principle in tree-like Resolution. This gives a new and simpler proof of the same lower bound established by...

In this note we show that the asymmetric Prover-Delayer game developed in [BGL10] for Parameterized Resolution is also applicable to other tree-like proof systems. In particular, we use this asymmetric Prover-Delayer game to show a lower bound of the form 2 logn) for the pigeonhole principle in tree-like Resolution. This gives a new and simpler proof of the same lower bound established by Iwama...

It is shown to be consistent with set theory that every set of reals of size א1 is null yet there are א1 planes in Euclidean 3-space whose union is not null. Similar results are obtained for circles in the plane as well as other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain maximal operators and a measure theoretic pigeonhole principle.

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...

We extend results of A. Haken to give an exponential lower bound on the size of resolution proofs for propositional formulas encoding a generalized pigeonhole principle. These propositional formulas express the fact that there is no one-one mapping from c ·n objects to n objects when c > 1. As a corollary, resolution proof systems do not p -simulate constant formula depth Frege proof systems.