Topics

• Digital Computations (fundamental classical models):
  Turing machines, register machines, word processing (groups and monoids), other machines
• Digital models of computation:
  cellular automata, other automata, tiling of the plane, polyominoes, snakes, neural networks, molecular computations
• Analog and Hybrid Computations:
  BSS machines, infinte cellular automata, real machines, quantum computing

In all these settings:

• frontiers between a decidable halting problem and an undecidable one in the various computational settings
• minimal universal codes:
  size of such a code, namely, for Turing machines, register machines, cellular automata, tilings, neural nets, Post systems, ...
• computation complexity of machines with a decidable halting problem as well as universal machines
• connections between decidability under some complexity class and completeness according to this class
• self-reproduction and other tasks
• universality and decidability in the real field