Service-Oriented Synthesis of Distributed and Concurrent Protocol Specifications

Algorithm 3

Partitioning procedure.

Procedure:  Partition_Parallel_Paths

Inputs: A PE-SPEC and an image of a fork state $s$ in the PE-SPEC model.

Outputs: Groups of parallel pathspartitioned at state $s$ and a set of sub-paths of each path in a group.

Steps:

(1) $G_1=G_2=\{\}$,

(2) for each transition $t$ outgoing from state $s$do

 (2.1) if   $t$, which is the first transition in an image of a parallel path $p$, is associated

   with a service primitive then$G_1=G_1\cup p$  else  $G_2=G_2\cup p$,

(3) for each path $p$ in $G_2$do

 (3.1) ${\text{SUB}}_p=\{\}\hspace{1em}\{$set of sub-paths of $p\}$,

 (3.2) $s_0=s$,

 (3.3) while ($s_0$ is not a joint or free state) do

       (3.3.1) $s_1=\text{successive}{(s_0)}_p$,

       (3.3.2) while ($s_1$ is not a joint or free state and the outgoing transition from $s_1$ is not

       associated with a receiving event) do

     (3.3.2.1) $s_1=\text{successive}{(s_1)}_p$,

       (3.3.3) ${\text{SUB}}_p={\text{SUB}}_p\cup$ subpath of $p$ from $s_0$ to $s_1$,

       (3.3.4) $s_0=s_1$.