### Table 4. A model checking algorithm for -calculus properties, where refinement is made locally on configurations, i.e., on abstract-states combined with properties. Here, the components of P and G are denoted as in Definition 6, resp. 1. Procedure Simplify is given in Table 3, Refine in

"... In PAGE 11: ... This procedure of simplification and local refinement is repeated until the property for the initial game-state is verified or falsified. The verification algorithm PropertyCheck is presented in Table4 and its used Refine-procedure, which calculates the local refine- ment, is presented in Table 5. Note that the initial abstraction in PropertyCheck can be imprecise (if every concrete state has an outgoing transition or if none of them has one), but this imprecision will be eliminated after refinement steps.... ..."

### Table 5. An algorithm for local refinement calculation, where the components of P are denoted as in Definition 6, resp. 1. The occurring procedures are explained in Section 4.

"... In PAGE 11: ... 1. Procedure Simplify is given in Table 3, Refine in Table5 , Add is explained in Section 4, and Heuristic is discussed in Section 5 in the abstract property-game. The transitions incoming/leaving such a new game-state ~ c0 split from ~ c are calculated by taking the transitions incoming/leaving ~ c into account.... In PAGE 11: ... This procedure of simplification and local refinement is repeated until the property for the initial game-state is verified or falsified. The verification algorithm PropertyCheck is presented in Table 4 and its used Refine-procedure, which calculates the local refine- ment, is presented in Table5 . Note that the initial abstraction in PropertyCheck can be imprecise (if every concrete state has an outgoing transition or if none of them has one), but this imprecision will be eliminated after refinement steps.... ..."

### Table 1. Comparison of procedural and algebraic abstraction.

1999

"... In PAGE 2: ... They can be combined and the type parameters duly replaced by the actual parameters, much the same way as in the application of functions. Table1 demonstrates the parallels between the two concepts. Table 1.... ..."

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### Table 3. Procedure UpdateAbstractSMDP()

2002

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### Table 4. Final version of instrumentation relations introduced by abstraction refine- ment.

2004

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### Table 4. Final version of instrumentation relations introduced by abstraction refine- ment.

2004

Cited by 5

### Table 3. Analysis with the refined abstraction, using awidening upto forpolyhedra

### TABLE II PERFORMANCE STATISTICS FOR ABSTRACTION AND REFINEMENT DEBUGGING FRAMEWORK

### Table I-Fibre and Bundle structural attributes and their abstraction/refinement.

### Table 10.11: PCM Abstract vs. Refined Comparison

2004