In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order logic as generic parameterized problems and show how this approach can be useful in studying both fixed-parameter tractability and intractability. For exampl...

This paper focuses on the problem of sliding mode control for delay-dependent stabilization criterion of bilinear state-delay systems. Based on the linear matrix inequality (LMI) method and a parameterized model transformation technique, we provide a sufficient condition for the existence of sliding surface and we give an explicit formula of sliding surface guaranteeing the asymptotic stability...

it is extremely challenging to measure first-order rate coefficients for soil nitrate transformation processes directly, either in the laboratory or in the field. in this study, an improved inverse method was proposed to optimize the first-order rate coefficients by considering the intermediate changing processes of the integrated functions. a numerical experiment was designed to test the accur...

We introduce tree-width for first order formulae φ, fotw(φ). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed parameter tractable, with parameter the length of the formula. This is done by translating a formula φ with fotw(φ) < k into a formula of the k-variable fragment L of firs...

We present an approach to knowledge compilation that transforms a function-free first-order Horn knowledge base to propositional logic. This form of compilation is important since the most efficient reasoning methods are defined for propositional logic, while knowledge is most conveniently expressed within a first-order language. To obtain compact propositional representations, we employ techni...

Collections, i. e., sets, bags, ordered sets and sequences, play a central role in UML and OCL models. Essential OCL operations like role navigation, object selection by stating properties and the first order logic universal and existential quantifiers base upon or result in collections. In this paper, we show a uniform representation of flat and nested, but typed OCL collections as well as str...