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We present a polynomial-time algorithm that obtains a set of AsymptoticLinear Programs (ALPs) from a given linear system S, such that one of theseALPs admits a feasible solution if and only if S admits a feasible solution. Wealso show how to use the same algorithm to determine whether or not S admits anon-trivial solution for any desired subset of its variables. S is allowed toconsist of linear constraints over real variables with integer coefficients,where each constraint has either a lesser-than-or-equal-to, or a lesser-than,or a not-equal-to relational operator. Each constraint of the obtained ALPs hasa lesser-than-or-equal-to relational operator, and the coefficients of itsvariables vary linearly with respect to the time parameter that tends topositive infinity.

Efficiently expressing feasibility problems in Linear Systems, as feasibility problems in Asymptotic-Linear-Programs