### Table 7: Variation of state-space size with bu er capacity

1998

"... In PAGE 16: ... They are: (a) a direct solver for relatively small models and (b) an iterative solver for large models (in the order of several hundreds of thousands of states). In this work, we use the iterative solver because of the largeness of the state-space size, which is illustrated in Table7 . The steady-state solvers provide information about the mean, variance, probability density function and probability distribution function of each of the performance variables, based on the steady-state state occupancy probabilities.... In PAGE 16: ... The state-space size of the resulting process is dependent on the number of input ports, bu er, and concentrator size. For example, the state-space size for a 16-input switch as a function of bu er size M with L = 8 is shown in Table7 . Observe the approximately linear growth in state-space size with increasing bu er size.... ..."

Cited by 3

### Table 1. The state space variables.

in An architecture for natural language dialog applications in data exploration and presentation domain

"... In PAGE 8: ... For example, most database retrieval tasks can be modelled efficiently by using forms, while more open-ended dialogues, such as enti- ties identification in corporate databases may be implemented more efficiently using state-machines. Below in the Table1 we describe state variables and variables values in our dialog management system for data retrieval, analysis and presentations tasks. Because the system is user centric orientated the values of some state space variables are nor fixed as in [21] but has some range of flexibility.... ..."

Cited by 2

### Table 1: Variation of state-space size with bu#0Ber capacity with a tagged port

1997

"... In PAGE 10: ... III SAN representation and model solution Having formulated the problem, the next step is to construct the appropriate Markov chains to compute the distribution of consecutive cell losses. Since these Markov processes are large #28on the order of tens of thousands of states, see Table1 #29, we use UltraSAN #5B28#5D, a SAN-based performance modeling and analysis tool, to generate the needed Markov processes, rather than construct them by hand. The SAN can precisely represent the FPS architecture, workload, and performance variables speci#0Ced abstractly in the previous section.... ..."

Cited by 5

### Table 2. Size of state space.

2002

"... In PAGE 8: ... Analysis Results After modeling the behavior of crowd members as de- scribed in section 4, and specifying anonymity properties as described in section 5, we used PRISM to perform prob- abilistic model checking of different system configurations and compute the relevant probabilities. Table2 describes the size of the state space for models of different size. The number of corrupt crowd members does not affect the size of the state space since all corrupt members are modeled as a single process (see section 4.... ..."

Cited by 32

### Table 2. Size of state space.

2002

"... In PAGE 8: ... Analysis Results After modeling the behavior of crowd members as de- scribed in section 4, and specifying anonymity properties as described in section 5, we used PRISM to perform prob- abilistic model checking of different system configurations and compute the relevant probabilities. Table2 describes the size of the state space for models of different size. The number of corrupt crowd members does not affect the size of the state space since all corrupt members are modeled as a single process (see section 4.... ..."

Cited by 32

### Table 6: State Space Sizes for Detailed Base Model Construction Methods

"... In PAGE 21: ... As can be seen from the #0Cgure, the marking behavior of even a small con#0Cguration of the example system is quite complex. Furthermore, as shown in Table6 , it grows in size rapidly as the number of bu#0Bers and processors considered increases. Dashes in the table represent state spaces that were too large to generate.... In PAGE 23: ... However, this construction method results in base models that become extremely large as the size of a system grows. For example, Table6 shows that the size of the resulting activity-marking space of the faulty multiprocessor model grows extremely rapidly as the number of processors and bu#0Ber stages is increased. Even if one considers only the marking behavior, the state space grows quickly, and becomes unman- ageable for most realistic applications.... In PAGE 29: ... The di#0Berences in state space size are dramatic for larger systems, as shown in Table 7. As with Table6 , dashes represent state spaces that were too large to generate. As can be seen from the table, generating detailed base models become impractical after only ten processors, but models for up to 500 processors can be generated when using reduced base model construction methods.... ..."

### Table 2. Total clique state space size of the three models

"... In PAGE 17: ...17 Table2 shows the total clique state space of the optimal junction trees used for solving each LIMID where the optimality criterion is clique state space size. The total clique state space size is de ned as P C2C Q X2C kXk, where C denotes the set of cliques of the junction tree and kXk denotes the number of states of variable X.... In PAGE 17: ... Table2 also shows the total clique state space size when each model is solved as an in uence diagram. The table shows that the DeepC and VOR- TEX models when considered as in uence diagrams cannot be solved on a standard 32 bits PC platform (each vehicle is equipped with a standard 32 bits PC platform running either Windows or Linux operating systems).... ..."

### Table 1. Development set results, sparse training data. Or- der 1 state-space model does not seem to learn the data very well and order 5 state-space model also has some problems. Both order 2 and 3 state-space models get slightly better results than the best n-gram model (of order 5).

### Table 1. Completely exploring state spaces with BFS and several reduction methods.

2006

"... In PAGE 13: ... The main question to investigate is therefore how C2c performs in comparison to C2s. Table1 depicts results obtained by completely exploring the state space of some models using BFS as search algorithm in combination with various reduction methods: no partial-order reduction at all (no), no action ignoring prevention (C2i), C2v, C2s and C2c. Note that C2i leads to an unsound reduction.... In PAGE 14: ... Completely exploring state spaces with BFS and several reduction methods. By comparing the two previous sets of experiments we observe the following phenomenon: in model marriers, algorithm BFS with C2c explores as many states as BFS with C2i ( Table1 ), while A* with C2c explores almost twice the states than A* with C2i (Table 2). In other words, the C2c proviso is refuting ample sets when the search algorithm is A* but not when it is BFS.... ..."

Cited by 3

### Table 1. Completely exploring state spaces with BFS and several reduction methods

"... In PAGE 13: ... The main question to investigate is therefore how C2c performs in compar- ison to C2s. Table1 depicts results obtained by completely exploring the state space of some models using BFS as search algorithm in combination with various reduction methods: no partial-order reduction at all (no), no action ignoring pre- vention (C2i), C2v, C2s and C2c. Note that C2i leads to an unsound reduction.... In PAGE 14: ...Intherestofthemodels both provisos work equally well. Bycomparingthetwoprevioussetsofexperiments we observe the following phenomenon: in the marriers model, algorithm BFS with C2c explores as many states as BFS with C2i ( Table1 ), while A* with C2c explores almost twice as many states as A* with C2i (Table 2). In other words, the C2c proviso is refuting Table 2.... ..."