Related papers: $\omega$-Regular Energy Problems
With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce generalized energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels…
We develop a $^*$-continuous Kleene $\omega$-algebra of real-time energy functions. Together with corresponding automata, these can be used to model systems which can consume and regain energy (or other types of resources) depending on…
The notion of comparison between system runs is fundamental in formal verification. This concept is implicitly present in the verification of qualitative systems, and is more pronounced in the verification of quantitative systems. In this…
The B\"uchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting condition. The standard solution to this problem involves adding an auxiliary clock…
We investigate the Cauchy problem for elliptic operators with $C^\infty$-coefficients at a regular set $\Omega \subset R^2$, which is a classical example of an ill-posed problem. The Cauchy data are given at the subset $\Gamma \subset…
The languages of infinite timed words accepted by timed automata are traditionally defined using Buchi-like conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore…
The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have…
A parameter method is introduced in order to estimate the relationship among the various variables of a system in equilibrium, where the potential energy functions are incompletely known or the quantum mechanical calculations very…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
This work considers a multiobjective version of the unit commitment problem that deals with finding the optimal generation schedule of a firm, over a period of time and a given electrical network. With growing importance of environmental…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
We introduce a novel technique to analyse unambiguous B\"uchi automata quantitatively, and apply this to the model checking problem. It is based on linear-algebra arguments that originate from the analysis of matrix semigroups with constant…
In this paper, we propose a novel framework for the synthesis of robust and optimal energy-aware controllers. The framework is based on energy timed automata, allowing for easy expression of timing constraints and variable energy rates. We…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the…
In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(\omega,\Omega) \times L^2(\omega,\Omega)/\mathbb{R}$, where $\omega$ belongs to the Muckenhoupt class $A_2$.…
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of…
In this paper we study the Boltzmann equation near global Maxwellians in the $d$-dimensional whole space. A unique global-in-time mild solution to the Cauchy problem of the equation is established in a Chemin-Lerner type space with respect…
The ever increasing adoption of mobile devices with limited energy storage capacity, on the one hand, and more awareness of the environmental impact of massive data centres and server pools, on the other hand, have both led to an increased…
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…