Second-Order Logic over Finite Structures – Report on a Research Programme

摘要

This paper reports about the results achieved so far in the context of a research programme at the cutting point of logic, formal language theory, and complexity theory. The aim of this research programme is to classify the complexity of evaluating formulas from different prefix classes of second-order logic over different types of finite structures, such as strings, graphs, or arbitrary structures. In particular, we report on classifications of second-order logic on strings and of existential second-order logic on graphs.