The paper presents novel, comprehensive and systematic methodology, which c
an be used to automate synthesis of cellular automata-based test pattern ge
nerators with phase shifters. First, a very fast and simple simulation fram
ework is proposed to either verify or generate maximum-length linear finite
state machines such as cellular automata or linear feedback shift register
s. Subsequently, a new framework is presented for efficient selection of ph
ase shifters that satisfy criteria of channel separation and circuit comple
xity. As shown in the paper, it is possible to synthesize, in a time effici
ent manner, very large cellular automata and their corresponding fast phase
shifters for built-in self-test applications with guaranteed structural an
d functional properties.