Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objects with bounded resources. This chapter consists of two independent parts. The first part is devoted to finite model theory; it is mostly a survey of logics tailored for computational complexity. The second part is devoted to dynamic structures with bounded resources. In particular, we use dynamic structures with bounded resources to model Pascal.

We explain and advance Levin's theory of average case completeness. In particular, we exhibit examples of problems complete in the average case and prove a limitation on the power of deterministic reductions.

The first algebraic average-case complete problem is presented. It isargDFDO the simplest natural averag1NDF" complete problem to date.