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Automatic Abstraction for Verification of Timed Circuits and Systems?

Mar 11, 2023

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Page 1: Automatic Abstraction for Verification of Timed Circuits and Systems?

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Page 2: Automatic Abstraction for Verification of Timed Circuits and Systems?

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Page 3: Automatic Abstraction for Verification of Timed Circuits and Systems?

clk+clk+

ack2−

x0.t+ x0.f+

x1.t+ x1.f+

ack2+x2.t+ x2.f+

ack1−

ack1+

clk+ clk+[12, 12]

[12, 12] [12, 12]

[1,2]

[0,1][0,1][0,1]

[1,2] [1,2]

[1,2][1,2]

[1,2]

[1,2]

clk+clk+

x0.t+ x0.f+

x1.t+ x1.f+

ack1−

ack1+

clk+ clk+[12, 12]

[12, 12] [12, 12]

[1,2]

[0,1][0,1][0,1]

[1,2] [1,2]

[1,2][1,2]

[1,2]

[1,2]

$

$

$$

clk+clk+

x0.t+ x0.f+

x1.t+ x1.f+

ack1−

ack1+

clk+ clk+[12, 12]

[12, 12] [12, 12]

[1,2]

[0,1][0,1][0,1]

[1,2] [1,2]

[2,4]

[1,2]

$

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Page 4: Automatic Abstraction for Verification of Timed Circuits and Systems?

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Page 7: Automatic Abstraction for Verification of Timed Circuits and Systems?

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Page 8: Automatic Abstraction for Verification of Timed Circuits and Systems?

l1 u1[ , ] l2 u2

l3 u3

a b c d

$

e f

[ , ]

[ , ]

d1d2

a b c d

d1

= [ , uu 32+ ]+l2 l3d2

= [ , uu 31+ ]+l1 l3

fe

transformation 1

a bl3 u3[ , ]

e fcd

l2 u2[ , ]l1 u1[ , ] $ cd e fd1

= [ , uu 32+ ]+l2 l3d2

= [ , uu 31+ ]+l1 l3

ba

d2d1

transformation 2� j�� � ´:����"� ©�WB© o=j)h¯]»cb_kjVXZ`¡h¯gV_a�1j�caY«gVXÝy!j)X�º¿z{µ

la u, a[ ] lb u, b[ ]

lc u, c[ ]

a b

$ $

clb lc

ua ucub

l = min( , )la +u = max( , )+

c

a b

l[ , u]

� j�� � ´:����"� ©#XE© o=j)hL]&cb_kj)XZ`¡hLg)_a�1j)caY\gOXZY=µ

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Page 9: Automatic Abstraction for Verification of Timed Circuits and Systems?

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