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.