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This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
The optimal power flow is an optimization problem used in power systems operational planning to maximize economic efficiency while satisfying demand and maintaining safety margins. Due to uncertainty and variability in renewable energy…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a…
Since the work of Polyanskiy, Poor and Verd\'u on the finite blocklength performance of capacity-achieving codes for discrete memoryless channels, many papers have attempted to find further results for more practically relevant channels.…
The minimum number of NOT gates in a logic circuit computing a Boolean function is called the inversion complexity of the function. In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that…
We consider the problem of minimization of sum transmission energy in cellular networks where coupling occurs between cells due to mutual interference. The coupling relation is characterized by the signal-to-interference-and-noise-ratio…
Mobile edge computing (MEC) can enhance the computing capability of mobile devices, and non-orthogonal multiple access (NOMA) can provide high data rates. Combining these two technologies can effectively benefit the network with spectrum…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
We develop a computation model for solving Boolean networks that implements wires through quantum ground-state computation and implements gates through identities following from angular momentum algebra and statistics. The gates are static…
The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction…
We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability…
In systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive…
We study the classical problem of minimizing the total weighted completion time on a fixed set of $m$ identical machines working in parallel, the $Pm||\sum w_jC_j$ problem in the standard three field notation for scheduling problems. This…
Real-time hierarchical energy-sharing markets are promising to coordinate large numbers of prosumers. Still, most existing clearing methods rely on linearized or DC power-flow models and do not explicitly handle reactive power or…
In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a…
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints.…
In this paper, we study the minimal cost constrained input-output (I/O) and control configuration co-design problem. Given a linear time-invariant plant, where a collection of possible inputs and outputs is known a priori, we aim to…