This paper deals with logical characterizations of picture languages of any dimension by syntactical fragments of existential second-order logic. Two classical classes of picture languages are studied: the class of recognizable picture languages, i.e. projections of languages defined by local constraints (or tilings): it is known as the most robust class extending the class of regular languages...

It is highly desirable for a computational model to have a logic characterization like in the seminal work of Büchi that connects MSO with finite automata. For example, weighted automata are the quantitative extension of finite automata for computing functions over words and they can be naturally characterized by a subfragment of weighted logic introduced by Droste and Gastin. Recently, cost re...

Deficiency in expressive power of the first-order logic has led to developing its numerous extensions by fixed point operators, such as Least Fixed-Point (LFP), inflationary fixed-point (IFP), partial fixed-point (PFP), etc. These logics have been extensively studied in finite model theory, database theory, descriptive complexity. In this paper we introduce unifying framework, the logic with it...

One of the fundamental results of descriptive complexity theory, due to Immerman [12] and Vardi [17], says that a class of ordered finite structures is definable in fixed-point logic if, and only if, it is computable in polynomial time. Much effort has been spent on the problem of capturing polynomial time, that is, describing all polynomial time computable classes of not necessarily ordered fi...

.................................................................................................................................. iii ACKNOWLEDGMENTS ............................................................................................................. iv TABLE OF CONTENTS................................................................................................................ v L...

In this paper we study the properties of systems of bounded arithmetic capturing small complexity classes and state conditions sufficient for such systems to capture the corresponding complexity class tightly. Our class of systems of bounded arithmetic is the class of secondorder systems with comprehension axiom for a syntactically restricted class of formulas Φ ⊂ Σ 1 based on a logic in the de...

Sensory evaluation is used to measure consciousness, and primarily developed in experimental and mathematical psychology. Sensory experiences can be reported using verbal (semantic) methods. This paper presents an overview of our semantic research achievements over the past decade, focusing on methodological attempts for substantiating the measure as a descriptive sensory analysis. Two types of...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

Ehrenfeucht-Fraı̈ssé games and their generalizations have been quite successful in finite model theory and yield various inexpressibility results. However, for key problems such as P 6= NP or NP 6= co-NP no progress has been achieved using the games. We show that for these problems it is already hard to get the board for the corresponding Ehrenfeucht-Fraı̈ssé game. We obtain similar results for t...