  Evidence and results suggesting that a Noether--like theorem for conservation
laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here
is to the maximal congruences rather than the automorphisms of the local
dynamics.
  We take the results of Takesue and Hattori (1992) on the space of additive
conservation laws in one dimensional cellular automata. In reversible automata,
we show that conservation laws correspond to the null spaces of certain
well-structured matrices.
  It is shown that a class of conservation laws exist that correspond to the
maximal congruences of index 2. In all examples investigated, this is all the
conservation laws. Thus we conjecture that there is an equality here,
corresponding to a Noether--like theorem.
