By Franz J. Rammig
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Intuitively, the successors of a node are the nodes with formulas the same as tail of the node and the predecessors of a node are the nodes with tails the same as formula of the node. The edge between a node and its successor is labeled with head of the node. To some sense, the resulting automaton is a flattened path pattern. Given an LTL formula r in a textual path pattern form, the function create_graph initiates the automaton construction procedure by applying split to the starting node with formula and head set to r and tail set to T!.
Far closer to M, it is possible to make the behavior which caused the erroneous counterexample disappear. For the refinement of we repeat the above procedure until a definite conclusion can be drawn. During this procedure, the initial abstraction will be refined more and more close towards M. The refinement can be done based on the information derived from erroneous counterexamples [19]. As a result, the refined model is obtained by splitting the abstract state causing the erroneous counterexample into two subsets of the states, each of which represents a new abstract state.
Is never matched. But the loop from B via A to B is acceptable because Consequently, both A and B are accepting states with such a constraint on B that the loop from B must go through A. ”. Otherwise, the loop will always matche x*yT! and thus can not match the infinite part of x*yT! at all. Note that in this automata translation procedure we do not need fairness constraints with respect to the (implicit) “U” operators in the given formula. The reason is Let A =f*gT! , thus in the resulting automaton (Figure 8) only the state B labeled with T!