An Analytical Comparison of the I-Test and Omega Test
The Omega test is an exact, (worst case) exponential time data dependence test. The I-Test is a polynomial time test, but is not always exact. In this paper we show the fundamental relationship between the two tests under conditions in which both tests are applicable. We show that Fourier-Motzkin Variable Elimination (FMVE), upon which the Omega test is based, is equivalent to the Banerjee Bounds Test when applied to single-dimensional array reference problems. Furthermore, we show the Omega Test’s technique to refine Fourier-Motzkin Variable Elimination to integer solutions (dark shadow) is equivalent to the I-Test’s refinement of the Banerjee Bounds Test (the interval equation). Finally, under the conditions we specify, we show the I-Test delivers an inconclusive answer if and only if the Omega test would require an exhaustive search to produce an exact answer (the so-called “Omega Test Nightmare”).
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