*Interactive Automaton - formalism of
neurocomputing*

Present-day computers are "universal".
Meanwhile they still have difficulties with some tasks which are elementary for
humans and other living beings. Maybe some basic principles are missed? What
does it mean universal and what does it mean computing? Two major concepts are
usually mentioned at the foundation: a Turing Machine and a Finite-State
Automaton. A Turing Machine is a rather specialized construct. Its application
to different domains is possible only by analogy. A Finite-State Automaton is
more generalized and mathematically formulated, but is said to have less
computational power. Extensive research was done into the issue of equivalence.
The general conclusion is that a Turing Machine, a Finite-State Automaton, and
other similar constructs have much in common, but each of them is best suited
for the particular class of applications.

The standard formalism for a Finite-State Automaton is
undoubtedly correct because it was checked on multiple domains, but very
inconvenient for some cases. Say, when a robot manipulates an object, the state
of the object, not the machine itself is changing.

A Finite-State Automaton is perfect for modelling in
general, but when it comes to modelling a real machine, the formalism of an
Interactive Automaton is better.

This is a more natural variant of a Finite-State
Automaton. Several improvements are suggested.

1. The concept of the environment is introduced. A
machine shouldn't hang in vacuum.

2. States are attached to the environment, not to the
machine and the number of states is infinite. This will make it computationally
as powerful as a Turing Machine. States of the machine are possible too, but as
an extension.

The most detailed description of a particular Finite-State
machine is provided by State Transition Table. It becomes redundant now.
Instead, it is replaced by the Action-Result List. Also the familiar concepts
of a state, an action, a transition, an event receive more elegant semantics. A
state belongs to the environment. An action is executed by the machine. A
result of the action will be a new state which depends on the current state.
Events are generated by the environment and perceived by the machine. For
example, the environment may notify the machine that a new state was
established. Each machine is defined by a list of associations Event-Reaction.
The latter is one of the machine's actions. Note that Action-Result is a
characteristic of the environment, while Event-Reaction - of the machine.

A well formulated theory can render conclusions which
immediately become practically useful. Several important concepts are hinted by
this formalism. If the machine keeps an internal copy of the environment, it
can have only a finite number of states. Gear that reduces an infinite set to a
finite one is called attention.

If the state of the machine is changing, this is
learning. For example, it may happen when the length of the Action-Result list
is changing.

This approach also explains why people like collective
thinking so much. In this case, a brain is interacting with another brain
rather than with the passive environment.

Copyright (c)
I. Volkov, December 29, 2015