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lecture6.pdf
Preview of P vs NP
🔗 Source: cs.umd.edu
📊 Size: 89 KB
📄 Pages: 6 pages
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Summary

Lecture 6 covers sparse languages and P vs NP, and the polynomial hierarchy. Key points include: a language L is sparse if there exists a polynomial p such that |L ∩{0, 1}n| ≤p(n), and any sparse language is in P/poly. Theorem 1 states an NP-complete language L is Turing-reducible to a sparse language iff NP ⊂ P/poly. Theorem 2 (Mahaney’s theorem) states an NP-complete language L is Karp-reducible to a sparse language iff P = NP. The polynomial hierarchy (PH) is defined as PH = ∪i≥0Σi = ∪i≥0Πi, where Σi and Πi are classes of languages defined using polynomial-time relations, and PH ⊆ PSPACE.

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Lecture 6 covers sparse languages and P vs NP, and the polynomial hierarchy.

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  • File Format: PDF
  • File Size: 89 KB
  • Pages: 6
  • Language: EN
  • Total Downloads: 46
  • Last Updated: 1 month ago

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