Related papers: An $\omega$-Algebra for Real-Time Energy Problems
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of…
We present a scalable approach to computing nonlinear balancing energy functions for control-affine systems with polynomial nonlinearities. Al'brekht's power-series method is used to solve the Hamilton-Jacobi-Bellman equations for…
Recently data trees and data words have received considerable amount of attention in connection with XML reasoning and system verification. These are trees or words that, in addition to labels from a finite alphabet, carry data values from…
Runge-Kutta formulas are some of the workhorses of numerical solving of differential equations. However, they are extremely difficult to generate; the algebra involved can be very complicated indeed. It is now standard, following the work…
We here investigate the model of interacting dark energy in the context of five dimensional brane cosmology. The effective equations of state of dark energy are evaluated for various choices of the variable time dependent cosmological…
The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique…
Quantum finite automata (QFAs) have been extensively studied in the literature. In this paper, we define and systematically study quantum B\"uchi automata (QBAs) over infinite words to model the long-term behavior of quantum systems, which…
We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of…
The present work is an attempt to understand and review existing methods of energy generation in electric vehicles in the modern day context. Previous works in the field have proposed various mechanisms of energy generation that are very…
A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…
In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on…
In this paper we discuss some physical applications of topological *-algebras of unbounded operators. Our first example is a simple system of free bosons. Then we analyze different models which are related to this one. We also discuss the…
An eikonal algebra ${\mathfrak E}(\Omega)$ is a C*-algebra related to a metric graph $\Omega$. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are…
We present a direct transformation of weak alternating $\omega$-automata into equivalent backward deterministic $\omega$-automata and show (1) how it can be used to obtain a transformation of non-deterministic B\"uchi automata into…
This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…
A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results…
We begin the systematic model theoretic study of $\mathrm{C}^*$-algebras using the tools of continuous logic.
Many important initial value problems have the property that energy is non-increasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for…
Energy system models based on linear programming have been growing in size with the increasing need to model renewables with high spatial and temporal detail. Larger models lead to high computational requirements. Furthermore, seemingly…
We consider the non-linear thermoelastic plate equation in rectangular domains $\Omega$. More precisely, $\Omega$ is considered to be given as the Cartesian product of whole or half spaces and a cube. First the linearized equation is…