Search and Optimization in Logic and Evolutionary Computing
The main objective of research is the comparison of constraint satisfaction and optimization strate- gies in logic and evolutionary programming and by integration of both paradigms to overcome limitations and increase efficiency.
With discrete (proof) construction methods like in computational logic concepts like similar- ity of programs can hardly be utilized as they lack a useful topological structure. The continuous approach as with neural networks allows efficient optimization strategies (e.g. gradient techniques) but lacks expressiveness which results in problems as with initialization and knowledge extraction.
Combining the analytic and the logic framework- i.e. embedding discrete models (e.g. proof trees) in continuous ones - also aims at understanding the topology of the space of algorithms for dealing with topics like optimization, stability and reuse of programs.
The investigations are to be based on a functional analytical, operator algebraic model of algorithms. Girard's Geometry of Interaction represents and characterizes (linear) proofs within a C*-algebra setting and our own work demonstrated how to model neural network within operator algebras.