  In this article we use the idea of algorithmic complexity (AC) to study
various cosmological scenarios, and as a means of quantizing the gravitational
interaction. We look at 5D and 7D cosmological models where the Universe begins
as a higher dimensional Planck size spacetime which fluctuates between
Euclidean and Lorentzian signatures. These fluctuations are governed by the AC
of the two different signatures. At some point a transition to a 4D Lorentzian
signature Universe occurs, with the extra dimensions becoming ``frozen'' or
non-dynamical. We also apply the idea of algorithmic complexity to study
composite wormholes, the entropy of blackholes, and the path integral for
quantum gravity.
