  \emph{Canonical (logic) programs} (CP) refer to normal logic programs
augmented with connective $not\ not$. In this paper we address the question of
whether CP are \emph{succinctly incomparable} with \emph{propositional
formulas} (PF). Our main result shows that the PARITY problem, which can be
polynomially represented in PF but \emph{only} has exponential representations
in CP. In other words, PARITY \emph{separates} PF from CP. Simply speaking,
this means that exponential size blowup is generally inevitable when
translating a set of formulas in PF into an equivalent program in CP (without
introducing new variables). Furthermore, since it has been shown by Lifschitz
and Razborov that there is also a problem that separates CP from PF (assuming
$\mathsf{P}\nsubseteq \mathsf{NC^1/poly}$), it follows that CP and PF are
indeed succinctly incomparable. From the view of the theory of computation, the
above result may also be considered as the separation of two \emph{models of
computation}, i.e., we identify a language in $\mathsf{NC^1/poly}$ which is not
in the set of languages computable by polynomial size CP programs.
