Parity Filter Automata

Parity filter automata are a class of two-st a te cellular aut omata on the intege r grid po ints of t he real line in which cells are updated serially from left to right in each time period ra.ther than 5YOchronously in parallel. Parity filter auto mata support large numbers of "par ticles," or persistent repeating configurations, and the collision of these particles is frequently a. "soliton" collision in which the particles in teract , bu t from which both emerge with t heir identit ies preser ved . This paper presen ts a theory of such par ity filter automata . Period and velocity theo rems for particles, existence and uniqueness theorems, conser vation and monotone nonconservation laws, durat ion and phase shifts in soliton collisions, and other results are proved.