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We have considered the weak precedence function (WPF) with an error relation (?), and this method is a modified version of Aho\u0027s error detecting simple precedence functions. We represent the three weak precedince relations (\u0026lesdot;, \u003edot;, ?) by two pairs of functions, and we call them the Extended Weak Precedence Functions (EWPF). We define the semi-strong equivalence (SSE) to reduce the number of error relations, and show an efficient algorithm to compute the EWPF in SSE level. We have shown an algorithm which transforms an unambiguous context free grammar to a grammar which has the EWPF. This algorithm is easy to implement. 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