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A new methodology is presented to solve a strongly nonlinear circuit, characterized by Piece-Wise Linear (PWL) functions, symbolically and explicitly in terms of its circuit parameters and is amenable to computer implementation. The method is based on a modified nodal formulation of piecewise linear circuit equations as a mixed Linear Complementarity Problem (MLCP). The technique of determinant-decision diagrams is applied to implement the symbolic transformation of the MLCP to the standard LCP. Complementarity-decision diagrams are used to represent the resulting LCP. Examples are presented that demonstrate the accuracy and efficiency of the proposed method.