  There is a parallelism between Shannon information theory and algorithmic
information theory. In particular, the same linear inequalities are true for
Shannon entropies of tuples of random variables and Kolmogorov complexities of
tuples of strings (Hammer et al., 1997), as well as for sizes of subgroups and
projections of sets (Chan, Yeung, Romashchenko, Shen, Vereshchagin,
1998--2002). This parallelism started with the Kolmogorov-Levin formula (1968)
for the complexity of pairs of strings with logarithmic precision. Longpr\'e
(1986) proved a version of this formula for space-bounded complexities.
  In this paper we prove an improved version of Longpr\'e's result with a
tighter space bound, using Sipser's trick (1980). Then, using this space bound,
we show that every linear inequality that is true for complexities or
entropies, is also true for space-bounded Kolmogorov complexities with a
polynomial space overhead.
