In: IEEE Trans. on Automatic Control, Vol. 41, No. 12, pages 1751-1778. 1996.
Abstract: In this paper, we give evolution equations for free-choice Petri nets which generalize the [max,+]-algebraic setting already known for event graphs. These evolution equations can be seen as a coupling of two linear systems, a [min,+]-linear system and a quasi-(+, x)-linear one. This leads to new methods and algorithms to: in the untimed case, check liveness and several other basic logical properties; in the timed case, establish various conservation and monotonicity properties.
Keywords: algebraic approach, free-choice Petri nets.
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