Results 241 to 250 of about 1,041,680 (279)

Jump Operators, Interactive Proofs and Proof Complexity Generators

2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)
A jump operator J in proof complexity is a function such that for any proof system P, J(P) is a proof system that P cannot simulate. Some candidate jump operators were proposed by Krajicek and Pudlak [63] and Krajicek [57], but it is an open problem whether computable jump operators exist or not.
openaire   +2 more sources

Proof Complexity and Beyond

2017
Workshop ...
openaire   +2 more sources

Complexity of Hard-Core Set Proofs

computational complexity, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu, Chi-Jen, Tsai, Shi-Chun, Wu, Hsin-Lung   +2 more
openaire   +1 more source

Proof-complexity results for nonmonotonic reasoning

ACM Transactions on Computational Logic, 2001
It is well-known that almost all nonmonotonic formalisms have a higher worst-case complexity than classical reasoning. In some sense, this observation denies one of the original motivations of nonmonotonic systems, which was the expectation taht nonmonotonic rules should help to speed-up the reasoning process, and ...
Egly, Uwe, Tompits, Hans
openaire   +1 more source

Algorithm Analysis Through Proof Complexity

2018
Proof complexity can be a tool for studying the efficiency of algorithms. By proving a single lower bound on the length of certain proofs, we can get running time lower bounds for a wide category of algorithms. We survey the proof complexity literature that adopts this approach relative to two \(\mathsf {NP}\)-problems: k-clique and 3-coloring.
openaire   +1 more source

Proof Complexity and Beyond

Oberwolfach Reports
Proof complexity is a multi-disciplinary research area that addresses questions of the general form “how difficult is it to prove certain mathematical facts?” The current workshop focussed on recent advances in our understanding that the analysis of an appropriately tailored concept of “proof” underlies many of the arguments in algorithms,
Albert Atserias, Meena Mahajan, Jakob Nordström, Alexander Razborov   +3 more
openaire   +2 more sources

Eisenstein’s Proof Using Complex Analysis

2015
1. Let p and q be two distinct positive odd primes and r the positive minimal residues modulo q; then we will have pr ≡ r ′ or \(\mathit{pr} \equiv -r^{{\prime}}\bmod q\), where r ′ again denotes the positive minimal residues modulo q.1 Thus we have $$\displaystyle{\frac{\mathit{pr}} {q} = \frac{r^{{\prime}}} {q} + f\quad \text{or}\quad = -\frac{r^{
openaire   +1 more source

RKU v1.1: Proof Complexity Interface——Resource-Bounded Proof Complexity and Probabilistically Checkable Proofs Unification

This paper extends RKU v1.0 framework, providing rigorous interface with Proof Complexity/PCP. Unifies RKU resolution resources $\mathbf{R}=(m,N,L,\varepsilon)$ with proof complexity: proof budget $L$ equivalent to proof size lower bounds, statistical indistinguishability bridges with probabilistic verification.
Ma, Haobo, Zhang, Wenlin
openaire   +1 more source

Proof Complexity Generators

The P vs. NP problem is one of the fundamental problems of mathematics. It asks whether propositional tautologies can be recognized by a polynomial-time algorithm. The problem would be solved in the negative if one could show that there are propositional tautologies that are very hard to prove, no matter how powerful the proof system you use.
openaire   +1 more source

Increasing the size and complexity of discrete 2D metallosupramolecules

Nature Reviews Materials, 2021
Heng Wang, Yiming Li, Na Li
exaly