Fixed Point vs. First-Order Logic on Finite Ordered Structures with Unary Relations

We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes a property valid for every unary relation definable by first-order logic over these classes which is peculiar to classes of ordered structures with unary relations. In a second step we show that this property itself can be expressed in fixed point logic and can be used to construct a non-elementary unary relation.

On the Fractal Nature of WWW and Its Application to Cache Modeling

The World Wide Web (WWW or Web) is growing rapidly on the Internet. Web users want fast response time and easy access to a enormous variety of information across the world. Thus, performance is becoming a main issue in the Web. Fractals have been used to study fluctuating phenomena in many different disciplines, from the distribution of galaxies in astronomy to complex physiological control systems. The Web is also a complex, irregular, and random system. In this paper, we look at the document reference pattern at Internet Web servers and use fractal-based models to understand aspects (e.g. caching schemes) that affect the Web performance.