Preprocessing
Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location g
Probabilistic Analysis
Probabilistic Program after Preprocessing
Start: f
Program_Vars: X₀
Temp_Vars:
Locations: f, g
Transitions:
g₀:f(X₀) -{0}> t₁:g(1) :|:
g₂:g(X₀) → [1/2]:t₃:g(0) :+: [1/2]:t₄:g(1) :|: 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀
Run classical analysis on SCC: [f]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
Sizebounds
(g₀,g), X₀: 1 {O(1)}
Run probabilistic analysis on SCC: [f]
Run classical analysis on SCC: [g]
MPRF for transition t₃: g(X₀) → g(Temp_Int₁₉) :|: X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ Temp_Int₁₉ ≤ 0 ∧ 0 ≤ Temp_Int₁₉ ∧ 1 ≤ X₀ of depth 1:
new bound:
2 {O(1)}
MPRF:
• g: [1+X₀]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:inf {Infinity}
g₀: 1 {O(1)}
g₂: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
Sizebounds
(g₀,g), X₀: 1 {O(1)}
(g₂,g), X₀: 1 {O(1)}
Run probabilistic analysis on SCC: [g]
Plrf for transition g₂:g(X₀) → [1/2]:t₃:g(0) :+: [1/2]:t₄:g(1) :|: 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀:
new bound:
2 {O(1)}
PLRF:
• g: 2⋅X₀
Use expected size bounds for entry point (g₀:f→[t₁:1:g],g)
Use classical time bound for entry point (g₀:f→[t₁:1:g],g)
Results of Probabilistic Analysis
All Bounds
Timebounds
Overall timebound:3 {O(1)}
g₀: 1 {O(1)}
g₂: 2 {O(1)}
Costbounds
Overall costbound: 4 {O(1)}
g₀: 0 {O(1)}
g₂: 4 {O(1)}
Sizebounds
(g₀,g), X₀: 1 {O(1)}
(g₂,g), X₀: 1 {O(1)}