  We describe a generalization of the group testing problem termed symmetric
group testing. Unlike in classical binary group testing, the roles played by
the input symbols zero and one are "symmetric" while the outputs are drawn from
a ternary alphabet. Using an information-theoretic approach, we derive
sufficient and necessary conditions for the number of tests required for
noise-free and noisy reconstructions. Furthermore, we extend the notion of
disjunct (zero-false-drop) and separable (uniquely decipherable) codes to the
case of symmetric group testing. For the new family of codes, we derive bounds
on their size based on probabilistic methods, and provide construction methods
based on coding theoretic ideas.
