Upper and Lower Loop Bound Estimation by Symbolic Execution and Loop - - PowerPoint PPT Presentation

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Upper and Lower Loop Bound Estimation by Symbolic Execution and Loop Acceleration Pavel Cadek 1 1 TU Wien, Austria Formal Methods in Computer-Aided Design 30 Oct - 2 Nov, 2018 Loop Bound Analysis Upper loop bound: max { n , 0 } Lower loop

SLIDE 1

Upper and Lower Loop Bound Estimation by Symbolic Execution and Loop Acceleration

Pavel ˇ Cadek1

1TU Wien, Austria

Formal Methods in Computer-Aided Design 30 Oct - 2 Nov, 2018

SLIDE 2

Loop Bound Analysis

i:=0 i<n i:=i+1 i>=n

Upper loop bound: max{n, 0} Lower loop bound: max{n, 0} Usage: worst case execution time memory consumption complexity analysis . . .

Pavel ˇ Cadek ( TU Wien, Austria ) FMCAD 2018 2 / 5

SLIDE 3

Symbolic Execution - Path Explosion

i:=0 i<n i>=n i:=i+1 . . . i<n i>=n

Path conditions: ϕ1 ≡ 0 ≥ n ϕ2 ≡ 0 < n ∧ 1 ≥ n ϕ3 ≡ . . . . . .

Pavel ˇ Cadek ( TU Wien, Austria ) FMCAD 2018 3 / 5

SLIDE 4

Loop Acceleration

i<n i:=i+1

i:=i+κ

i<=n

Pavel ˇ Cadek ( TU Wien, Austria ) FMCAD 2018 4 / 5

SLIDE 5

Combination

i:=0 κ>0 i:=i+κ κ==0 i<=n i>=n

Path conditions: ϕ1 ≡ κ = 0 ∧ 0 ≥ n ϕ2 ≡ κ > 0 ∧ κ ≤ n ∧ κ ≥ n = ⇒ κ = max{n, 0}

Pavel ˇ Cadek ( TU Wien, Austria ) FMCAD 2018 5 / 5