Generalized juntas and NP-hard sets

NP-Hard Sets are Superterse Unless NP is Small

Frequency of Correctness versus Average Polynomial Time and Generalized Juntas

We prove that every distributional problem solvable in polynomial time on the average with respect to the uniform distribution has a frequently self-knowingly correct polynomialtime algorithm. We also study some features of probability weight of correctness with respect to generalizations of Procaccia and Rosenschein’s junta distributions [PR07b].

Trainyard is NP-hard

Recently, due to the widespread diffusion of smart-phones, mobile puzzle games have experienced a huge increase in their popularity. A successful puzzle has to be both captivating and challenging, and it has been suggested that this features are somehow related to their computational complexity [5]. Indeed, many puzzle games – such as Mah-Jongg, Sokoban, Candy Crush, and 2048, to name a few – a...

Relationships between NP-sets, Co-NP-sets, and P-sets relative to random oracles

In the present paper we prove that relative to random oracle A (with respect to the uniform measure) the following three assertions hold: (1) there is a pair of disjoint NP A-sets which are separable by no P A-set, (2) there is a pair of disjoint Co-NP A-sets which are separable by no P A-set and (3) there is an innnite Co-NP A-set having no innnite NP A-subset

Candy Crush is NP-hard

We prove that playing Candy Crush to achieve a given score in a fixed number of swaps is NP-hard.