← 研踪 PaperTrailarXiv:2611.07308 · v1
Quadratic-Time Barriers from Self-Referential SAT
首次提交 2026-11-05 09:50
版本更新 2026-11-05 09:50
雷达观测 2026-11-06 10:04
摘要
Under the self-referential $K$-SAT exhaustive-search hypothesis (SRK-ESH), no uniform deterministic algorithm computes exact longest common subsequence or standard edit distance on binary strings in $O(n^{2-η})$ time for any fixed $η>0$, where $n$ is the longer sequence length. The same exclusion holds for one-dimensional dynamic time warping on $\{0,1,2,4,8\}$ with absolute-difference cost and for five-symbol dynamic time warping with the discrete metric. We derive Orthogonal Vectors hardness in polylogarithmic dimension by splitting the variables of the logarithmic-width source formula into two halves. Existing sequence reductions have polynomial overhead in the dimension. Their output lengths and construction times allow a fixed saving in the target exponent to yield a fixed proportional saving in the source exponent.
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v1 · 2026-11-05 09:50 · 最新观测版本
Quadratic-Time Barriers from Self-Referential SAT
Under the self-referential $K$-SAT exhaustive-search hypothesis (SRK-ESH), no uniform deterministic algorithm computes exact longest common subsequence or standard edit distance on binary strings in $O(n^{2-η})$ time for any fixed $η>0$, where $n$ is the longer sequence length. The same exclusion holds for one-dimensional dynamic time warping on $\{0,1,2,4,8\}$ with absolute-difference cost and for five-symbol dynamic time warping with the discrete metric. We derive Orthogonal Vectors hardness in polylogarithmic dimension by splitting the variables of the logarithmic-width source formula into two halves. Existing sequence reductions have polynomial overhead in the dimension. Their output lengths and construction times allow a fixed saving in the target exponent to yield a fixed proportional saving in the source exponent.
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