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Since the first exposition of the complex Frobenius structures (\cite{N}),there have been considerable development and many new applications on thissubject(see \cite{G}, \cite{H1},\cite{HT}, \cite{S}, \cite{Web},\cite{W} andreferences therein). Inspired by complex Frobenius structures, L. H{\"o}rmanderintroduced a class of first order overdetermined systems of partialdifferential equations (\cite{H1}) and established existence theorems. Thispaper is devoted to the construction of resolution for the solution sheaves ofthese overdetermined systems considered in \cite{H1}. A sufficient conditionfor global exactness is obtained, which leads to gluing technique for localsolutions of the overdetermined systems by solving Cousin type problems. Inaddition, we also prove local solvability of the Treves complex withoutassuming the non-degeneracy of the Levi form.

Formally Integrable Structures I. Resolution of Solution Sheaves