On two open problems of 2-interval patterns

Two Open Problems on Effective Dimension

Effective fractal dimension was defined by Lutz [13] in order to quantitatively analyze the structure of complexity classes. The dimension of a class X inside a base class C is a real number in [0,1] corresponding to the relative size of X ∩ C inside C. Basic properties include monotonicity, so dimension 1 classes are maximal and dimension 0 ones are minimal, and the fact that dimension is defi...

On the computational complexity of 2-interval pattern matching problems

The focus of this paper is on the computational complexity of pattern matching problems over set of 2-intervals. These problems occur in the context of molecular biology when a structured pattern, i.e., a RNA secondary structure given in the form of a 2-interval pattern, has to be found in a sequence database. We show that 3nding a 2-interval pattern in a set of 2-intervals is a NP-complete pro...

On Pre-θ-Open Sets and Two Classes of Functions

Open problems for equienergetic graphs

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

Settling Some Open Problems on 2-Player Symmetric Nash Equilibria

Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the following; it was stated by Papadimitriou in 2007: find a non-symmetric Nash equilibrium (NE) in a symmetric game. We show that this problem is NP-complete and ...