The paper considers methods of forward and backward symbolic modeling which are used for solution of verification tasks for basic protocols systems. Besides of algorithms for state space search detailed in model checking works, the main task of symbolic modeling is implementation of transition from one state class to the next. Such a transformation is realized by predicate transformers. In the current work, algorithms of forward and backward predicate transformers have been built for numeric, symbolic, and lists data structures. Transformers are considered as functions which derive from given formula a new one that defines state class of the system after transition made by given basic protocol.

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