FREE-CHOICE PETRI NETS - AN ALGEBRAIC APPROACH

In this paper, we give evolution equations for free-choice Petri nets which generalize the [max, +]-algebraic setting already known for even t graphs, These evolution equations can be seen as a coupling of two l inear systems, a (min, +)-linear system and a quasi-(+, x)-linear one, This leads to new methods and algorithms to: in the untimed case, che ck liveness and several other basic logical properties; in the timed c ase, establish various conservation and monotonicity properties;in the stochastic case, check stability, i.e., the fact that the marking rem ains bounded in probability, and construct minimal stationary regimes, The main tools for proving these properties are graph theory, idempot ent algebras, and ergodic theory.