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SamuelSchlesinger merged 2 commits into from
Oct 30, 2026
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doc(pcp): clarify the perfect-completeness hardness roadmap #1829

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doc(pcp): clarify the perfect-completeness hardness roadmap
SamuelSchlesinger Oct 30, 2026
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Merge main into the perfect-completeness roadmap clarification
SamuelSchlesinger Oct 30, 2026
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5 changes: 2 additions & 3 deletions ROADMAP.md
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Expand Up @@ -323,9 +323,8 @@ DLOGTIME-uniform AC⁰ under explicit conventions.

- **Håstad's optimal MAX-E3SAT hardness** ([#886]): for `0 < ε < 1/8`, NP-hardness of
distinguishing satisfiable E3-CNF formulas from those where every assignment satisfies at most
`7/8 + ε` of the clauses. This needs the reduction to MAX-E3LIN;
Raz–Holenstein parallel repetition for small-soundness Label Cover; and
the perfect-completeness reduction.
`7/8 + ε` of the clauses. This needs Raz–Holenstein parallel repetition for small-soundness
Label Cover and Håstad's separate perfect-completeness construction for MAX-E3SAT.
- The FGLSS clique-hardness reduction and its amplification, retaining the exact gap and
reduction runtime.
- Gap and approximation-preserving reductions, APX/PTAS/FPTAS, inapproximability consequences of
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