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Finding symmetries of algebraic system nets

Junttila T.A.

Fundamenta Informaticae

1999

Vol. 37, Nr 3

269-289

The problem of finding symmetry information from algebraic system nets prior to the reach-ability graph generation is studied. The approach presented is based on wellformedness of transition descriptions, meaning that some data types in a net may be used in a symmetric way. Permutations on the domains of such data types produce symmetries on the state space level of the net, which in turn can be exploited during the reachability analysis. To ensure that the transitions behave symmetrically with respect to the chosen data domain permutations, a sufficient compatibility condition between data domain permutations and the algebraic terms used as transition guards and arc annotations is proposed. The solution is a general and flexi-ble one as it does not fix the set of applicable operations, enabling the design of customized net classes. To help the process of deciding whether a term is compatible with a data domain permutation, an approximation rule for the compatibility condition is given.