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Mount Usu / Sarobetsu post-mined peatland
From left: Crater basin in 1986 and 2006. Cottongrass / Daylily
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Principle of optimality (最適性原理)= Bellman equation, discovered by Richard Bellman (1953)= dynamic programming equation Bellman, Richard Ernest (1920–1984) Theoretical computer scienceComputational complexity theory (計算複雑性理論)Classifying computational problems according to their resource usage and their related problems⇒ algorithm P versus NP problem (P問題とNP問題)= one of the seven Millennium Prize Problems (unsolved problem in computer science)Def. P or class P: the general class of questions that some algorithm can answer in polynomial time |
an algorithm that can be solved in polynomial time is present
that can determine whether a solution is correct or not in polynomial time when a solution is given in advance, although no algorithm has been found that solves the problem efficiently in polynomial time |
Boole George (1815-1864, England)
differential equations and algebraic logic Boolean algebraAxiom
1' = 0 → 1' = 1'•1 = 1•1' = 0 a + 1 = 1 → a + 1 = a + (a + a') = (a + a) + a' = a + a' = 1 a•0 = 0•a = 0 → a•0 = 0•a, a•0 = a(aa') = (aa)a' = aa' = 0 a + ab = a → a + ab = a•1 + ab = a(1 + b) = a•1 = a a(a + b) = a → a(a + b) = aa + ab = a + ab = a a(a + b + c) = a → aa + ab + ac = (aa + ab) + ac = a + ac = a a + bc = (a + b)(a + c) → a + bc = a(a + b + c) + bc = a(a + b) + ac + bc = a(a + b) + c(a + b) // Q Solve simultaneous equation a + x = 1, ax = 0A (x = a') is a root because of axiomatic system (a + a' =1)
set x0 as a root |
Law. De Morgan's law (1)→ (ab)' = a' + b'Pr. (a' + b') + ab = (a' + b' + a)(a' + b' + b) = (b' + 1)(a' + 1) = 1•1 = 1
while (a' + b')ab = a'ab + b'ab = 0•b + 0•a = 0 + 0 = 0 Law. de Morgan's law (2)→ (a + b)' = a'b'Pr. (a + b)' = [(a')' + (b')']' = [(a'b')']' = a'b' // Table. Case that Boolean algebra that has only specific factors (0, 1) + 0 1 • 0 1 ' ------- ------- ---- 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 Table. Set {a, b} → subset φ, U = {a, b}, {a}, {b} 0 = π, 1 = U, 2 = {a}, 3 = {b} + 0 1 2 3 • 0 1 2 3 ' ------------- ------------- ---- 0 0 1 2 3 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 2 3 1 0 2 2 1 2 1 2 0 2 2 0 2 3 3 3 1 1 3 3 0 3 0 3 3 2 |
1969 Thompson K: developing the OS for mini-computer PDP-7 (DEC)
= beginning of UNIX Ex. ATT System V, UCB BSD, IBM AIX 1973 Richie D: unix kernel re-written by C language1991.10.5 Linus T (Finland): opned Linux distributed freely, independent of unix-OS system → becoming popular EWS (engineering workstation)
Past: office computer = EWS ↔ personal computer (PC)
Present:
one of the UNIX OSs, developed by Univercity of Carfornia, Berkeley
characterzied by high-spec job control projects and standards of six computer items, including desktop and network environments, drawn up common API proposed by UNIX vendors |