Research objectives and content
A A + B: The research field of the applicant is the branch of logic called finite model theory (or. descriptive complexity theory). Its main goal is to understand the relationship between the computational complexity of a problem and its logical expressibility. In the last years there has been growing work on bounded arithmetic related to desriptive complexity theory. The group of logicians in Sevilla investigates subsystems of arithmetic, so that, during the planned s in Sevilla of three months, the applicant hopes to acquire a deeper knowledge and understanding in bounded arithmetic. at least in those issues related to descriptive complexity theory and hence, to his own research. At the same time, he wants to impart his knowledge in finite model theory and to help the group in Sevila to reach the frontier of research, in particular. in those parts of the field where the applicant himself or his group in Freiburg have been active during t last years: these include
? problems of expressive power of fixed-point logics. normal fo its applications to complete problems for complexity classes. ? the study of logics with generalized quantifiers and its rela to fixed-point logics and to complexity classes with oracles ? the relationship between various DATALOG like languages and " cal" formal languages.
Traning content (objective, benefit and expected impact)