Research Article
An Efficient Siphon-Based Deadlock Prevention Policy for a Class of Generalized Petri Nets
Algorithm 1
A deadlock prevention policy for
PR based on improved elementary siphons.
Input: an PR | Output: a live controlled system | () begin; | () Compute the set of SMS and their corresponding augmented siphons | () Find the set of elementary siphons , dependent siphons , and the set of virtual | resources . | () for ( to ) do | () Compute the augmented complementary set of elementary siphons ,. | () end for | () Compute the set of linear inequality constraints expressed by state vectors from according to (4), where is an incidence | an incidence matrix, binary matrix restricts the PN marking vector to its components corresponding to places , and | , , otherwise ; , . | () According to Definition 29, modify the matrix to be matrix . | () Get the set of GMEC expressed by the marking vector according to (10), that is, , where vector is the restriction | of marking to operation places. | () if () then | () Find a set of for elementary siphons by solving the LPP according to Theorem 30, where . | () Get the adjusted GMEC , where . | () end if | () According to Definition 24 and the above set of GMEC, add the set of monitors for the corresponding to the net , and the | obtained controlled system is denoted by . | () output | () end. |
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