Thesis Chapters by Andrej Ilić
The ability of randomness to increase polynomial time computational power has been a subject of c... more The ability of randomness to increase polynomial time computational power has been a subject of controversy for the past 40 years. More precisely, the problem lies in determining whether every problem decidable in bounded-error polynomial time (BPP) can be decided in deterministic polynomial time (P). The answer to this question initially appeared to be negative, fueled by the success of Miller-Rabin pri-mality test in the late 1970s, along with many other "successes of randomization". However, the consensus on the issue gradually reversed, guided by the theoretical work of Adleman [1], Sipser [18], Lautemann [11] and Widgerson [9, 13], among others. In a recent paper [2], Agarwal provided strong support for the BPP=P view by demonstrating a deterministic polynomial primality test. This paper will follow this shift of consensus through the related theoretical developments that motivated it.
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Thesis Chapters by Andrej Ilić