Further Explanations on "SAT Requires Exhaustive Search"
CoRR(2024)
摘要
Recently, Xu and Zhou [2023] introduced a constructive approach for exploring
computational hardness, proving that SAT requires exhaustive search. In light
of certain misinterpretations concerning the contributions and proofs in that
paper, we focus on providing detailed explanations in this work. We begin by
delineating the core innovation of the constructive approach, shedding light on
the pivotal concept of algorithm designability. We address the overlooked
white-box diagonalization method and highlight the concept of an almost
independent solution space. In response to specific misunderstandings, such as
the concerns surrounding the assumptions of Lemma 3.1, we offer comprehensive
clarifications aimed at improving the comprehension of the proof. We are
grateful for the feedback received on our prior paper and hope this work can
foster a more well-informed discussion.
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