Title: The possibility of constructing a relativistic space of information states based on the theory of complexity and analogies with physical space-time,
Abstract: The possibility of calculation of the conditional and unconditional
complexity of description of information objects in the algorithmic theory of
information is connected with the limitations for the set of the used languages
of programming (description). The results of calculation of the conditional
complexity allow introducing the fundamental information dimensions and the
partial ordering in the set of information objects, and the requirement of
equality of languages allows introducing the vector space. In case of optimum
compression, the "prefix" contains the regular part of the information about
the object, and is analogous to the classical trajectory of a material point in
the physical space, and the "suffix" contains the random part of the
information, the quantity of which is analogous to the physical time in the
intrinsic reference system. Analysis of the mechanism of the "Einstein's clock"
allows representing the result of observation of the material point as a word,
written down in a binary alphabet, thus making the aforesaid analogies more
clear. The kinematics of the information trajectories is described by the
Lorentz's transformations, identically to its physical analog. At the same
time, various languages of description are associated with various reference
systems in physics. In the present paper, the information analog of the
principle of least action is found and the main problems of information
dynamics in the constructed space are formulated.