J.-M. Steyaert Amphi 10 : Introduction aux Syst mes distribués : P2P

P=N P ?

Les circuits
Source Intel
SoC = System on Chip
microprocesseurs de PC
téléphones, DVD, TV, GPS
Source Intel 2
B
B:= {⊤,⊥} := {1,0}:= {V, F },
Bm
Bpm, p ≥1
BmBm≥1
2mmB
¬(0) = 1,¬(1) = 0
0∧0 = 0 0 ∧1 = 0 1 ∧0 = 0 1 ∧1 = 1
0∨0 = 0 0 ∨1 = 1 1 ∨0 = 1 1 ∨1 = 1
0|0 = 1 0|1 = 1 1|0 = 1 1|1 = 0
α(x, y, z) = x y z.
x
y
z
α(x, y, z)
Une porte de base (NAND)
Source Cadence Design Systems
6

(m+ 1) 2m
2m
f(x) =
ν(x), ν(x) = Pbi2i
x0 1
y0 1 0 1
z0 1 0 1 0 1 0 1
α(x, y, z) 0 1 0 1 0 0 1 1
0 1 x0 1
0 1 0 1 y0 1 0 1
0 1 0 1 0 1 z0 1
0 1 0 1 α(x, y, z) 0 1 0 1
O(2m/m)
p(x, y, z)x, y, z z, x, y
x
y
z
pz(x, y, z)
(x, y, z) (z, x, y)
S
+.¬S
a+b=b+a a.b =b.a
a+ (b+c) = (a+b) + c a.(b.c) = (a.b).c
a.(b+c) = (a.b) + (a.c)a+ (b.c) = (a+b).(a+c)
a+a=a a.a =a¬¬a=a
¬0 = 1 ¬1 = 0 a+¬a= 1 a.¬a= 0
1 + a= 1 0.a = 0
0 + a=a1.a =a
¬(a+b) = ¬a.¬b¬(a.b) = ¬a+¬b

{a, b, c, d, ...} A
λ=a λ =¬a
λ1λ2...λh
λ1+λ2+... +λh
f m
Am
{+, ., ¬}
{+,¬} {., ¬} {α}
{+, ., ¬}
x+y=¬(¬x.¬y)
{., ¬} ¬x=α(x, 0,1)
x.y =α(x, y, 0) {α}
{+, .}
.
+ +
¬y x z
x

(a1+a2)(b1+b2)...(j1+j2)
210 = 1024
ab...j
m2m/2 log2m
m
Circuit: propagation de retenue
+
+
a0
b0
r= 0
0s0
+
+
1
a
1
b1
s
r1Pour n bits
temps n
+
+
2
a
2
b2
s
r2
r3
12