### Table 1. Model Checking Statistics without/with State Space Reduction (SSR), Live Variable Analysis (LVA) No SSR With SSR

"... In PAGE 18: ... For Scenario 3, the results show that although the state space reduction strategies suffer some overhead when the number of clients is small, they are beneficial when the number of clients (flows) increases. For scenario 4, there was a state space explosion without SSR (indicated by asterisks in Table1 ), whereas the model exploration became quite tractable with SSR, although the state space does increase when the deadlock avoidance protocol is present, showing that there are potential trade-offs in the checking required for one property (blocking factors) when checking for another property (deadlock) is avoided through use of a proved protocol [8]. 7.... ..."

### Table 1: Comparison of Parametric Model Checking Methods proposed by model property decidable? time complexity

1998

"... In PAGE 1: ... One of the considerable approaches to such problems is restricting the expressing power of Timed Automata. Comparison between existing parametric model checking methods are summarized in Table1 . For example, [6] proposed a parametric model checking algorithm in that both a model and a property are written in finite parametric timed automata (PTA) with one integer clock variable.... In PAGE 3: ... Finally, we perform the extension of DDFS to derive the weakest parameter condition in order that the given model never executes invalid runs specified by the given property. Class hierarchies for models and properties in Table1 are shown in Figs. 1, 2, and 3.... ..."

Cited by 2

### Table 1. Considered Model-Checking Problems

2003

"... In PAGE 9: ... Number of Back-Level Edges computation and the number of discovered back-level edges (see Table 3). For our set of experiments we chose several standard software protocols (see Table1 for a list). All systems are parametrized: the Philosophers problem by the number of philosophers, the Elevator by the number of floors served, the Peterson, Leader election, and the Token ring by the numberof participating processes.... In PAGE 9: ... All systems are parametrized: the Philosophers problem by the number of philosophers, the Elevator by the number of floors served, the Peterson, Leader election, and the Token ring by the numberof participating processes. The LTL formulas speci- fying the checked properties are given in Table1 together with the answer to the model-checking problem. As stressed in the introduction, the main reason for the development of a distributed model-checking algorithms is typically to increase the available memory trading it for time.... ..."

Cited by 11

### Table 1. Considered Model-Checking Problems

"... In PAGE 9: ... Number of Back-Level Edges computation and the number of discovered back-level edges (see Table 3). For our set of experiments we chose several standard software protocols (see Table1 for a list). All systems are parametrized: the Philosophers problem by the number of philosophers, the Elevator by the number of floors served, the Peterson, Leader election,andtheToken ring by the numberof participating processes.... In PAGE 9: ... All systems are parametrized: the Philosophers problem by the number of philosophers, the Elevator by the number of floors served, the Peterson, Leader election,andtheToken ring by the numberof participating processes. The LTL formulas speci- fying the checked properties are given in Table1 together with the answer to the model-checking problem. As stressed in the introduction, the main reason for the development of a distributed model-checking algorithms is typically to increase the available memory trading it for time.... ..."

### Table 4 Effect of VM assist and ECPS:VM on CMS batch processing on Systeml370 Model 148 configured like Model 145

"... In PAGE 12: ... The same job stream was run on a Model 148 configured like the Model 145. The results, summarized in Table4 , provide insight into the effects of VM assist and ECPS/VM during CMS execution. IV.... ..."

### Table 3 Effect of VM assist on CMS batch processing on Systeml370 Model 145

"... In PAGE 12: ... CMS vir- tual machines issue relatively few privileged instructions or SU- pervisor calls, so it is interesting to consider how VM assist affects CMS environments. Table3 shows how VM assist can affect a CMS batch processing application on a System/370 Model 145. The same job stream was run on a Model 148 configured like the Model 145.... ..."

### Table 2. Checks and verification Here, the problem of space and time complexity of the finite state machines (automata) for recognizing languages arises. In general, the classical regular language operators (concatenation, alternative, repetition) do not introduce any exponential growth of the state space of a parsing finite state automaton. However, behavior protocols employ also the and- parallel, composition, and adjustment operators that introduce exponential complexity of the resulting automata which might lead to the state explosion problem. In fact, the composition and adjustment operators behave better than the and-parallel operator in terms of the required state space as they comprise synchronization of events, thus reducing the interleaving of traces.

2002

Cited by 112

### Table 1 An overview of complexity results for the model-checking problem

"... In PAGE 2: ... In the presence of the X-operator, the expected duality occurs: The fragment with F, X plus and and the one with G, X plus or are both NP-hard. Table1 gives an overview of our results. The top row refers to the sets of Boolean operators given in Definition 2.... In PAGE 15: ... Further work should find a way to handle the open xor cases from this paper as well as from [1,3]. In addition, the precise complexity of all hard fragments not in bold-face type in Table1 could be determined. Furthermore, we find it a promising perspective to use our approach for obtaining a fine-grained analysis of the model-checking problem for more expressive logics, such as CTL, CTL*, and hybrid temporal logics.... ..."

### Table 1: Validation results The results in Table 1 indicate that the time needed to compile an ESML model is small compared to the time required to generate the complete reachability graph of a model. The number of transitions in the di erent models are small compared to the number of states generated for each model. The number of transitions in a model has no bearing on the size of the state space of a model. For example the two elevator models have the same number of transitions although the state space of the 4- oor elevator model is 20 times as large as that of the 3- oor model. The X-Windows model behaved especially badly: after 1 hour 56 minutes (7000 seconds) and about 5 million states the available memory of the machine (128 Mb) was exhausted and the state generation had to be aborted. It can be argued that during model checking it is in general unnecessary to generate the complete reachability graph because a given CTL formula may be either validated or

"... In PAGE 87: ... The models1 were compiled and the resulting transition system executed to generate the complete state space of each model. In Table1 the comparative gures obtained are given. The following ve categories of comparison were chosen: 1The validation system is used as part of a graduate course on model checking at the University of Stellenbosch.... In PAGE 90: ...7 Optimisations From the validation results given in the previous chapter ( Table1 ) it is clear that a state explosion occurs during the validation of complex models. In this chapter model reduction techniques are described to counter this state explosion problem.... ..."

### Table 3. Comparison of target reliability levels

2005

"... In PAGE 8: ... The target reliability level for assessment is different from that appropriate for the design stage due to (a) economic considerations, which lead to the use of less conservative criteria for assessment as the increment in cost of upgrading an existing structure is much larger than that for increasing safety at the design stage (b) social considerations, such as heritage values and disruption of occupants and activities caused by an intervention that do not affect the design of new structures (c) sustainability considerations; for example, reduction of waste and recycling, more appropriate with the rehabilitation of existing structures. Table3 compares target lifetime reliability levels in various codes and standards currently in use. The engineer dealing with the assessment of an existing structure must decide among the available tables which of the values are most suited and best applied to the solution of the problem at hand as the estimated probability of failure associated with a project is very much a function of the costs as well as an understanding of the issues, modelling the data, etc.... ..."