Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: #R##N#Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,···,xn and determines whether or not the output of the formula is identically 0 (as a formal expression)#R##N#Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,···,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression).#R##N##R##N##R##N##R##N#One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3.  also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally,  obtain an exponential lor bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lor bounds for the depth of pure circuits re previously known.)
['Ran Raz', 'Amir Shpilka']
I am writing a research paper on a idea Deterministic polynomial identity testing in non-commutative models
[{"from": "human", "value": "I am writing a research paper on a idea Deterministic polynomial identity testing in non-commutative models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: #R##N#Non-commutative arithmetic formulas: The algorithm gets as an input an arithmetic formula in the non-commuting variables x1,\u00b7\u00b7\u00b7,xn and determines whether or not the output of the formula is identically 0 (as a formal expression)#R##N#Pure arithmetic circuits: The algorithm gets as an input a pure set-multilinear arithmetic circuit (as defined by Nisan and Wigderson) in the variables x1,\u00b7\u00b7\u00b7,xn and determines whether or not the output of the circuit is identically 0 (as a formal expression).#R##N##R##N##R##N##R##N#One application is a deterministic polynomial time identity testing for set-multilinear arithmetic circuits of depth 3.  also give a deterministic polynomial time identity testing algorithm for non-commutative algebraic branching programs as defined by Nisan. Finally,  obtain an exponential lor bound for the size of pure setmultilinear arithmetic circuits for the permanent and for the determinant. (Only lor bounds for the depth of pure circuits re previously known.)"}]