We show that the problem of showing that a cusped 3-manifold M is not hyperbolic is in NP, assuming -RECOGNITION is in coNP. To this end, we show that IRREDUCIBLE TOROIDAL RECOGNITION lies in NP. Along the way we unconditionally recover SATELLITE KNOT RECOGNITION lying in NP. This was previously known only assumin…
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7 results for “coNP”
The study shows a way to represent Seifert fiber space groups with a limited field size.
problem Representing Seifert fiber space groups with non-abelian .
method Using a triangulation of Seifert fiber spaces and a quotient to limit the field size.
result The lens space recognition problem is shown to be in coNP for Seifert fiber space input.
We developed an efficient algorithm to factorize knots.
problem Computing the prime factorization of knots efficiently.
method Introduced an edge-ideal triangulation to represent knots and developed an algorithm using Regina.
result Our algorithm works well for knots up to 19 crossings and provides new complexity results.
New research shows deep learning struggles with hard problems due to biased data generation.
problem Deep learning's limitations in solving computationally hard problems.
method Proved that polynomial-time sample generators for NP-hard problems sample from easier sub-problems.
result Machine learning models trained on biased datasets overestimate their accuracy for hard problems.
The paper improves regret lower bounds for communicating MDPs.
problem Regret lower bounds for communicating MDPs.
method Lower bound proof and optimization problem formulation.
result Regret lower bound becomes significantly more complex in communicating MDPs.
We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). For hyperbolic integer homology spheres this comes with the definition, and for Seifert fibered integer homology spheres this is well known. We prove t…
Paper proves neural networks can be approximated using interval bounds.
problem Verifying safety and robustness of neural networks.
method Introduces interval universal approximation (IUA) theorem for neural networks.
result Neural networks can be approximated using interval bounds for any continuous function and squashable activation functions.