Preprocessing
Probabilistic Analysis
Probabilistic Program after Preprocessing
Start: f
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f, g
Transitions:
g₀:f(X₀,X₁) -{0}> t₁:g(X₀,X₁) :|:
g₂:g(X₀,X₁) → [1/2]:t₃:g(X₀-1,X₁) :+: [1/2]:t₄:g(X₀,X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
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: X₀ {O(n)}
(g₀,g), X₁: X₁ {O(n)}
Run probabilistic analysis on SCC: [f]
Run classical analysis on SCC: [g]
MPRF for transition t₃: g(X₀,X₁) → g(X₀-1,X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
• g: [X₀]
MPRF for transition t₄: g(X₀,X₁) → g(X₀,X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
• g: [X₁]
Classical Approximation after Lifting Classical Results
All Bounds
Timebounds
Overall timebound:X₀+X₁+1 {O(n)}
g₀: 1 {O(1)}
g₂: X₀+X₁ {O(n)}
Costbounds
Overall costbound: inf {Infinity}
g₀: inf {Infinity}
g₂: inf {Infinity}
Sizebounds
(g₀,g), X₀: X₀ {O(n)}
(g₀,g), X₁: X₁ {O(n)}
(g₂,g), X₀: 2⋅X₀ {O(n)}
(g₂,g), X₁: 2⋅X₁ {O(n)}
Run probabilistic analysis on SCC: [g]
Results of Probabilistic Analysis
All Bounds
Timebounds
Overall timebound:X₀+X₁+1 {O(n)}
g₀: 1 {O(1)}
g₂: X₀+X₁ {O(n)}
Costbounds
Overall costbound: 2⋅X₀+2⋅X₁ {O(n)}
g₀: 0 {O(1)}
g₂: 2⋅X₀+2⋅X₁ {O(n)}
Sizebounds
(g₀,g), X₀: X₀ {O(n)}
(g₀,g), X₁: X₁ {O(n)}
(g₂,g), X₀: X₀ {O(n)}
(g₂,g), X₁: X₁ {O(n)}