Related papers: Computing the Best Case Energy Complexity of Satis…
In this paper, we initiate study of the computational power of adaptive and non-adaptive monotone decision trees - decision trees where each query is a monotone function on the input bits. In the most general setting, the monotone decision…
A long-investigated problem in circuit complexity theory is to decompose an $n$-input or $n$-variable Majority Boolean function (call it $M_n$) using $k$-input ones ($M_k$), $k < n$, where the objective is to achieve the decomposition using…
The problem of attaining energy efficiency in distributed systems is of importance, but a general, non-domain-specific theory of energy-minimal scheduling is far from developed. In this paper, we classify the problems of energy-minimal…
The characterization of the global maximum of energy efficiency (EE) problems in wireless networks is a challenging problem due to the non-convex nature of investigated problems in interference channels. The aim of this work is to develop a…
Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is…
The power system of the future will be governed by complex interactions and non-linear phenomena at small time-scales, that should be studied more and more through computationally expensive software simulations. To solve the abovementioned…
Energy is often the most constrained resource in networks of battery-powered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy…
We study the problem of routing vehicles with energy constraints through a network where there are at least some charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations by determining routes as…
In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function $f$ is…
In order for quantum computations to be done as efficiently as possible it is important to optimise the number of gates used in the underlying quantum circuits. In this paper we find that many gate optimisation problems for approximately…
Boolean networks are a general model of interacting entities, with applications to biological phenomena such as gene regulation. Attractors play a central role, and the schedule of entities update is a priori unknown. This article presents…
We establish new separations between the power of monotone and general (non-monotone) Boolean circuits: - For every $k \geq 1$, there is a monotone function in ${\sf AC^0}$ that requires monotone circuits of depth $\Omega(\log^k n)$. This…
We present a constructive SAT-based algorithm to determine the multiplicative complexity of a Boolean function, i.e., the smallest number of AND gates in any logic network that consists of 2-input AND gates, 2-input XOR gates, and…
We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions $F$ and a Boolean function $f$, determine if $f$ is in the clone generated by $F$, i.e., if it can be expressed by a circuit with…
The maximal clique enumeration (MCE) problem has numerous applications in biology, chemistry, sociology, and graph modeling. Though this problem is well studied, most current research focuses on finding solutions in large sparse graphs or…
The minimum number of inputs needed to control a network is frequently used to quantify its controllability. Control of linear dynamics through a minimum set of inputs, however, often has prohibitively large energy requirements and there is…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution…
In duty-cycled wireless sensor networks, the nodes switch between active and dormant states, and each node may determine its active/dormant schedule independently. This complicates the Minimum-Energy Multicasting (MEM) problem, which has…
We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the…