Structural measures for games and process control in the branch learning model

Process control problems can be modeled as closed recursive games.
Learning strategies for such games is equivalent to the concept of
learning infinite recursive branches for recursive trees. We use this
branch learning model to measure the difficulty of learning and
synthesizing process controllers. We also measure the difference
between several process learning criteria, and their difference to
controller synthesis. As measure we use the information content
(i.e. the Turing degree) of the oracle which a machine need to get the
desired power.

The investigated learning criteria are finite, EX-, BC-, Weak BC- and
online learning. Finite, EX- and BC-style learning are well known from
inductive inference, while weak BC- and online learning came up with
the new notion of branch (i.e. process) learning. For all considered
criteria - including synthesis - we also solve the questions of their
trivial degrees, their omniscient degrees and with some restrictions
their inference degrees. While most of the results about finite, EX-
and BC-style branch learning can be derived from inductive inference,
new techniques had to be developed for online learning, weak BC-style
... mehrlearning and synthesis, and for the comparisons of all process
learning criteria with the power of controller synthesis.