An algebraic proof of the real number PCP theorem
نویسندگان
چکیده
منابع مشابه
Reading group: proof of the PCP theorem∗
Let Σ be a finite alphabet. An instance of the label cover problem for Σ is: • a bipartite graph (V1, V2, E), • for every (u, v) ∈ E, a function πu,v : Σ→ Σ. A solution to an instance is a pair of mappings s1 : V1 → Σ and s2 : V2 → Σ such that for all (u, v) ∈ E, πu,v(s1(u)) = s2(v). Proposition 1. Label cover over a 3-element alphabet is NP-hard. Definition 1. A (strong) Mal’cev condition (L,Σ...
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Probabilistically checkable proofs are proofs that can be checked probabilistically by reading very few bits of the proof. In the early 1990s, it was shown that proofs could be transformed into probabilistically checkable ones with only a modest increase in their length. The initial transformations, though elementary, were a little too complex. A recent work due to Irit Dinur gives a dramatical...
متن کاملReading group: proof of the PCP theorem∗
Let Σ be a finite alphabet. An instance of the label cover problem for Σ is: • a bipartite graph (V1, V2, E), • for every (u, v) ∈ E, a function πu,v : Σ→ Σ. A solution to an instance is a pair of mappings s1 : V1 → Σ and s2 : V2 → Σ such that for all (u, v) ∈ E, πu,v(s1(u)) = s2(v). Proposition 1. Label cover over a 3-element alphabet is NP-hard. Definition 1. A (strong) Mal’cev condition (L,Σ...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2017
ISSN: 0885-064X
DOI: 10.1016/j.jco.2016.11.006