Remarks on generalized uncertainty principle induced from constraint system

The extended commutation relations for a generalized uncertainty principle have been based on the assumption of the minimal length in position. Instead of this assumption, we start with a constrained Hamiltonian system described by the conventional Poisson algebra and then impose appropriate second class constraints to this system. Consequently, we can show that the consistent Dirac brackets for this system are nothing but the extended commutation relations describing the generalized uncertainty principle.