Discrete Meets Continuous, Again
نویسنده
چکیده
This report collects some contributions about issues related to the notion of sampling invariance that has been introduced in [FR05, FR06], of which the present report can therefore be considered a follow-up and a complement. In particular: we compare the expressiveness of the language TRIO against that of MTL (and MITL), by also showing a result about the expressiveness of non-strict temporal operators; we characterize behaviors of bounded variability and formulas that preserve the bounded variability requirement; we compare the notion of sampling invariance with that of digitization [HMP92]; we discuss how to describe the runs of a timed automata with TRIO formulas; we provide an example of application of the sampling invariance techniques to a simple verification problem; we summarize several related works on the expressiveness, decidability, and complexity of formalisms that are somewhat related to the TRIO temporal logic.
منابع مشابه
Discrete and Continuous: Two sides of the same?
How deep is the dividing line between discrete and continuous mathematics? Basic structures and methods of both sides of our science are quite different. But on a deeper level, there is a more solid connection than meets the eye.
متن کاملContinuous Discrete Variable Optimization of Structures Using Approximation Methods
Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...
متن کاملDISCRETE SIZE AND DISCRETE-CONTINUOUS CONFIGURATION OPTIMIZATION METHODS FOR TRUSS STRUCTURES USING THE HARMONY SEARCH ALGORITHM
Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discret...
متن کاملDISCRETE AND CONTINUOUS SIZING OPTIMIZATION OF LARGE-SCALE TRUSS STRUCTURES USING DE-MEDT ALGORITHM
Design optimization of structures with discrete and continuous search spaces is a complex optimization problem with lots of local optima. Metaheuristic optimization algorithms, due to not requiring gradient information of the objective function, are efficient tools for solving these problems at a reasonable computational time. In this paper, the Doppler Effect-Mean Euclidian Distance Threshold ...
متن کاملA continuous approximation fitting to the discrete distributions using ODE
The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...
متن کاملA novel technique for a class of singular boundary value problems
In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...
متن کامل