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ure 3: Two pairs of vehicle trajectories, where the first one is non-colliding, and the second one

Towards formal verification of neural networks

  • 1.
    ( 7 0) 1 0 - 07- - 70 8 80 7 2- - 7 8 - 8 - 8 -2-
  • 2.
    • -. .. . . • - - - - - • -. . . . . . . . , . . . . • - . - - - -
  • 3.
    • E) 055 4 0 1 0 2 5 4 1 2 0 50 ) 0 2 1 2 A 2 0 ( . • E 54 5 4 2 52 2 0 2 A 2421C 2 0 ( . • G
  • 4.
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  • 5.
    . . ... . . . • . , ., . , . . . . . , , . . . ., • . . . . . . . . . . , ., . (. , .. . . ) .
  • 6.
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  • 7.
    (() • 1 3, : ,: : 2 : 1 : : ( , ,1 : , 1 3 . . : , :, 2 ) ., , : ,: , : : , . 1 . ∀"# . " − "′ < ( ⇒ * " − *("′) < - ( , , : ,: , : : , " − "′ < ( ⇒ * " − *("′) < - 2
  • 8.
    (() • ) ?? . = .= ?= ? = = =? = . ? ? C ? ? ? 1 ? C 1 =?. =. . . ? F • = C. . . ? .? . ? C C C C • .? . H ? = C. ? ? . ? = =? • , .? . H = .? • ? // / / . = C H ( ? =
  • 9.
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  • 10.
    ) ( • -. : . : • . - , : - . - - . : . - - - • . , • : , . , . 0 1 1 0 1
  • 11.
    • ? :2,3( 1 I E E = • - = E A = 2,3 A =A • 2,3 I E I E <= < I ? • 2 3 = := = = < E= • , E < I E A < ? : 2,3 • 0E A - A ( < E EE : = : = E = < < M R = P = ) P = E = P : E E= = : = +
  • 12.
    + + ++ + + • : : : , : , • : : ,: : : , / . . = . : , : . : B + . : : : : / = . : ::, : : ,/ : A :
  • 13.
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  • 15.
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  • 16.
    - - - -- - • 5 H H 0 : C 0H 0=LM M H 8 A H G HM C M A M H A M A H H MP EL H 1 G M 0 A M H 10 ) ( CMM L. PPP L C M H M = M H ))(+ +-, • . 5 ( C H R MC M M H M A G A P E H G M L A H LM G H M • . 3 = L A MR • . : L 4R 0: " 12308 = L H HM L • 12308 / 1 HM 2 G 3 0=LM M H 8 A H G HM
  • 17.
  • 18.
    ( ) ) ( •) • ) : : , A A F . A : : :A : ,C AC C : , A :: ,C AC C = = = AC C = = : A GAEAC E C , A : : A = : ( AC C = = : = : A ,C : A AC C :: . ..
  • 19.
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  • 20.
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  • 21.
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  • 23.
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  • 25.
    • 2 =T 0 /=LLA 1 1 GG 3 G = = J DA ALBAL 7AG KGAR, . ABB A MJG AL BJL AL BS C AAK A L=G A JL M 0. ( + D K, =LR JLC = M + ( ) D KM, C D J C S = TT 7AG KGAR0= ( + • , = L JL A JGG M J = J = A MSM A BJL = A = L L=B .0. • , GJ =G CGJ =G = ALM=L =G LJ M AMM • , " 57. MJG AL AR A A J D= GA 7A5: • 57. 5 A=L 7A=G .L D A • 57. MJG AL M M =GGS =MA J =G M KGAR A DJ
  • 26.
    • , =(-- 2 = = =A A A = = 2 2 =A = 2 =2 = =D = 2= . • . 2 2= AA 2A 2 . 2 2A H I H • ) D A A = 2 = 2 A A ,0 A D 2 A 2A A = • 2 = . = ,0 A D = =A = 2A A • 0 A 2 2= = 2 2 A A D
  • 27.
    • : FC6 B F B 6 -/) B A C : 6 / - 6 A C 0 F / - / F • 6 0 F B 6 -/) B A • , A 6 C B :CC ( B B BA AB 6 • + BCA CB A A A B C 6 B C 6 A 6B • !" = ∑%& ∈( )",+!+ A !+ ∈ , • ( B A B . ( B A B • -" ≤ !" ≤ /" A !" ∈ , ∪ 1 • : B A C B A BB C α ∶ , ∪ 1 → ℝ B : C: C ∀!+ ∈ 1. -+≤ α(!+) ≤ /+ 6 CA C B C B C: A 6B C A C B
  • 28.
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  • 29.
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  • 30.
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  • 31.
    - - - -- I L B E E F F E I E= 4 B N B E + B E ( I 5, IEBL E F BB = N F I I ) 5EBL 13 N B E I I =E = N I • I E A L = E E P I E= EL = N 4 1 E F = 4 1 = I B IEB E 0= I B I 02 .,50-1. • I B I = B E E F 005 0 B 0 = I B 5 I E = F I = N I 5, IEBL B I 5E I =E E I F EF E 3 I 3 I
  • 32.
    - - - -- • • ure 3: Two pairs of vehicle trajectories, where the first one is non-colliding, and the second one