### Table 1: Combined algorithm for incremental model refinement via deterministic annealing

2001

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### Table 1 summarizes the relationships between computations and models presented in this paper. Linearizability

1998

"... In PAGE 16: ...Table1 : Model-computation relationships linearizability SC coherence P-RAM-A P-RAM PC-G WO TSO PSO Figure 3 p p p p p p p p p Figure 4 p p p p p p p p Computation 1 p p p p p p p Computation 3 p p p Computation 4 p p p Computation 2 p p p p Computation 5 p p p p p Computation 6 p p p p Computation 7 p p p p p [2] S.... ..."

Cited by 3

### Table 5. ProB refinement checking using singleton failures

2005

"... In PAGE 13: ... (It is not necessary to make this distinction for trace refinement, since the traces model does not distinguish internal and external choice.) Some empirical results can be found in Table5 . All experiments were run on-the-fly, i.... ..."

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### Table 2. ProB refinement checking and size of refinement relation

2005

"... In PAGE 9: ...ref is a refinement thereof. Refinement checking Table2 are the results of performing various refinement checks on these machines. Entries marked with an asterisk mean that no pre- vious consistency checking was performed, i.... ..."

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### Table 2. ProB refinement checking and size of refinement relation

2007

"... In PAGE 13: ...erver example, while ServerR.ref is a refinement thereof. 7.2 Refinement checking Table2 are the results of performing various refinement checks on these machines. Entries marked with an as- terisk mean that no previous consistency checking was performed, i.... ..."

### Table 7. Algorithm to check for EMB

1998

"... In PAGE 37: ...Table 7. Algorithm to check for EMB The algorithm, which is shown in Table7 , is an adaptation to our framework of the algorithm described in [13] (which could be applied to the functional semantic models of finite-state terms of G), which is in turn a variant of the algorithm proposed in [29] to solve the relational coarsest partition problem. Given a labeled transition system with state space S representing the union of the integrated semantic models of two finite-state terms of G to be checked for EMB, or the integrated semantic model of a finite-state term of G to be minimized with respect to EMB, the idea of the algorithm is to repeatedly refine the current partition until this is a strong EMB.... In PAGE 38: ...By following the proposal of [29], this algorithm can be implemented in O(m log n) time and O(m + n) space where n is the number of states and m is the number of transitions. It is worth noting that a variant of the algorithm in Table7 can be used to compute the coarsest ordinary lumping [37] of the Markovian semantics of a given term, hence allowing for the determination of performance measures by solving a smaller Markov chain which is equivalent to the original one. Definition 5.... ..."

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### 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 4. Refinement checking on the already expanded state space with FDR

2005

"... In PAGE 11: ...8.1 was then run on the same hardware as for the earlier experiments to check CSP trace refinement and the results can be found in Table4 . Timings do not include the time needed to load the CSP file, but include the compilation, normalization and checking time of FDR.... ..."

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### Table 3 Summary of the parameters used in describing the complexity of Refine-Plan

1995

"... In PAGE 45: ...) Then we have d = N P f v Per-invocation cost of Refine-Plan: Trp itself can be decomposed into four main components: Trp = Test + Tcons + Ttract + Tsol; where Test, is the establishment cost (including the cost of selecting the open goal to work on), Tsol is the cost of solution constructor, Ttract is the cost of tractability refinement, and Tcons is the cost of consistency check. A summary of all the parameters used in the complexity model above can be found in Table3 . Armed with this model of the search space size and refinement cost, we will now look at the effect of the various ways of instantiating each step of the Refine-Plan algorithm on the search space size and the cost of refinement.... ..."

Cited by 111

### Table 6 Goal refinement predicates Goal refinement

"... In PAGE 15: ... In partic- ular, our formal framework supports all phases of the require- ments analysis process described in the paper, including goal modeling. Thus, firstly, we introduce predicates for goal/task refinement and resource decomposition ( Table6 ). Predicate service(s) holds if s is a service.... ..."

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