金丝雀
发表于 2025-3-23 13:21:26
Resolution Chap. 3 and Chap. 8. First we describe the most common restrictions placed on the type of resolution refutations, that is regular and tree-like resolution refutations (Sect. 2.1), then we prove a non-trivial size upper bound (Sect. 2.2) and finally we move to the complexity measures known as width and asymmetric width (Sect. 2.3).
rods366
发表于 2025-3-23 13:52:50
Space in Polynomial CalculusIn this chapter we consider in detail the propositional proof system ., briefly introduced in Sect. 1.1.2. We introduce some complexity measures—size, degree, monomial space and total space—and we show some techniques useful to prove lower bounds on those.
Immunization
发表于 2025-3-23 21:04:38
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capillaries
发表于 2025-3-24 01:06:54
Interlude: Cover GamesLet’s put aside proof complexity for a moment and, in this chapter, we will focus on some properties of bipartite graphs.
paltry
发表于 2025-3-24 06:08:40
Some Graph-Based FormulasWe now show some further applications of the general theorems to prove space lower bounds from Chap. 3 and Chap. 4. That is we see how to prove monomial and resolution total space lower bounds for random .-CNF formulas (Sect. 7.2), the pigeonhole principle over a bipartite graph (Sect. 7.3) and Tseitin formulas (Sect. 7.4).
伪造者
发表于 2025-3-24 08:26:40
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Thyroid-Gland
发表于 2025-3-24 14:10:28
he understanding of molecular pathogenesis.Covers all major .New research has shown that neuroendocrine tumors are more common than previously thought. Progress in our understanding of the molecular pathogenesis of these not-so-rare cancers has resulted in renewed interest in developing innovative
seduce
发表于 2025-3-24 17:32:30
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反复拉紧
发表于 2025-3-24 19:29:53
he understanding of molecular pathogenesis.Covers all major .New research has shown that neuroendocrine tumors are more common than previously thought. Progress in our understanding of the molecular pathogenesis of these not-so-rare cancers has resulted in renewed interest in developing innovative
AWRY
发表于 2025-3-25 01:51:14
Ilario Bonacinahe understanding of molecular pathogenesis.Covers all major .New research has shown that neuroendocrine tumors are more common than previously thought. Progress in our understanding of the molecular pathogenesis of these not-so-rare cancers has resulted in renewed interest in developing innovative