Compositional Mining of Multiple Object API Protocols through State Abstraction

Algorithm 2

The algorithm to extract the typestates for a super type from the typestates of its implementing subtypes.

Input:   𝑀=(𝑄,Σ,𝛿,𝜆,𝑆,𝐹) as typestates of type 𝑡

Output:   𝑀_𝑠=(𝑄_𝑠,Σ_𝑠,𝛿_𝑠,𝜆_𝑠,𝑆_𝑠,𝐹_𝑠) as typestates of super type 𝑠 of 𝑡

(1) initialize an empty FSM 𝑀_𝑠

(2) initialize an empty set of transitions worker

(3) foreach 𝑞∈𝑆  do

(4)   mark 𝑞 as visited

(5)   foreach 𝑒=(𝑞,𝑚,𝑞^′) such that 𝑚∈Σ_𝑠  do

(6)    add 𝑒 to worker

(7)   endfor

(8) endfor

(9) while there is a 𝑒=(𝑞,𝑚,𝑞^′) in worker do

(10)  remove 𝑒  from worker

(11)  if 𝑞^′ is not visited then

(12)   mark 𝑞^′ as visited

(13)   foreach 𝑒^′=(𝑞^′,𝑚^′,𝑞^′′) such that 𝑚^′∈Σ_𝑠  do

(14)    add 𝑒^′ to worker

(15)   endfor

(16)  endif

(17)  foreach 𝑝∈cl(𝑀,Σ_𝑠,𝑞) such that 𝑝≠𝑞  do

(18)   add (𝑞,𝑚,𝑝) to 𝑀_𝑠

(19)  endfor

(20) remove duplicated transitions in 𝑀_𝑠

(21)  return 𝑀_𝑠

Procedure  cl(𝑀,Σ_𝑠,𝑞)

(1) 𝑤𝑜𝑟𝑘𝑒𝑟=𝑟𝑒𝑠𝑢𝑙𝑡={𝑞}

(2) while there is a state 𝑝  in 𝑤𝑜𝑟𝑘𝑒𝑟  do:

(3)  add 𝑝 to result

(4)  remove 𝑝  from worker

(5)  foreach (𝑝,𝑎,𝑟)∈𝛿  such that 𝑎∈Σ−Σ_𝑠  do:

(6)   if 𝑟∉ result then:

(7)     add 𝑟 to worker

(8)   endif

(9)  endfor

(10)  endwhile

(11)  return result