Behavior and Instantiation of High–Level Net Processes

Abstract

Processes for high-level nets N are often defined as processes of the low-level net Flat(N) which is obtained from N via the well-known flattening construction. This low-level notion of processes for high-level nets, however, is not really adequate, because the high-level structure is completely lost. For this reason we have introduced in a previous paper a new notion of high-level net processes for high-level nets which captures the high-level structure. The key notion is a high-level occurrence net K, which generalizes the well-known notion of occurrence nets from low-level to high-level nets. In contrast to the low-level case we consider high-level occurrence nets together with a set of initial markings of the input places. In this paper we show under which conditions the behavior of low-level occurrence nets and processes can be generalized to the high-level case. A key notion is the instantiation L of a high-level occurrence net K, where L is a low-level subnet of the flattening Flat(K) with isomorphic net structures of L and K. One of our main results characterizes under which conditions a high-level occurrence net - and hence a high-level net process - has unique and nonoverlapping instantiations and can be represented by the union of all its instantiations.