Towards Light-Weight Probabilistic Model Checking

Table 1

Property patterns and their PRISM and MRMC translations.

Property in natural language	PRISM translation	MRMC translation
𝑝ℎ𝑖 will eventually hold, until then 𝑝𝑠𝑖 holds with a probability ⋈𝑝	P⋈𝑝  [psi  U  phi]	P{⋈𝑝}  [psi  U  phi]
𝑝ℎ𝑖 will hold within time bound [𝑡1, 𝑡2], until then 𝑝𝑠𝑖 holds with a probability ⋈𝑝	P⋈𝑝    [psi  U[t1, t2]  phi]	P{⋈𝑝}  [psi  U[t1, t2]  phi]
𝑝ℎ𝑖 always holds with a probability ⋈𝑝	P⋈𝑝  [G  phi]	P{⋈𝑝}  [!(tt  U  !(phi))]
𝑝ℎ𝑖 always holds within time bound [𝑡1, 𝑡2] with a probability ⋈𝑝	P⋈𝑝  [G[t1, t2]  phi]	P{⋈𝑝}  [!(tt  U[t1, t2]!(phi))]
𝑝ℎ𝑖 is always followed by 𝑝𝑠𝑖 with a probability ⋈𝑝	P⋈𝑝  [G  (phi  =>  P  >=  1  [true  U  psi])]	P{⋈𝑝}  [!(tt  U  !(phi  =>  P  >=  1  [tt  U  psi]))]
𝑝ℎ𝑖 is always followed by 𝑝𝑠𝑖 within time bound [𝑡1, 𝑡2] with a probability ⋈𝑝	P⋈𝑝  [G  (phi  =>  P  >=  1  [true  U[t1, t2]  psi])]	P{⋈𝑝}  [!(tt  U  !(phi  =>  P  >=  1  [tt  U[t1, t2]  psi]))]
𝑝ℎ𝑖 holds infinitely often with a probability ⋈𝑝	P⋈𝑝  [G  (P  >=  1  [true  U  phi])]	P{⋈𝑝}  [!(tt  U  !(P  >=  1  [tt  U  phi]))]
The expected accumulated reward until 𝑝ℎ𝑖 holds is ⋈𝑟	R⋈𝑟  [true  U  phi]
The expected accumulated reward until 𝑝ℎ𝑖 holds within t time units is between 𝑟1 and 𝑟2		E[t][r1,  r2][phi]