Permutation Combination (PC) based parsing algorithm of Knowledge Provider System (KPS) and Grammatical Rules (GR) based parsing algorithm of Automated Knowledge Provider System (AKPS) has been compared using the Time complexity and Space complexity. ``Big-O'' notation has been utilized by the Time function T(n) and Space function DSAPACE (T, X) to describe the time complexity and space complexity of both algorithms. Further it is clarified that PC based parsing system (KPS) is a subset of GR based parsing system(AKPS). The function T(n) and T(n, m) represents the equation of both algorithms of Knowledge Provider System and both the equations have been used in mathematical optimization to prove that one is subset of another. Hence, we can propose a Hybrid Knowledge Provider System (HKPS) that would combine the advantages of both PC based system and GR based system in terms of time complexity.
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