### Table 5. State-space statistics.

2001

"... In PAGE 47: ... Evaluations of the logistics domain paint a picture of the recognition accuracy once the state-space has been adequately explored and most of the indexing structures have been created. The statistics for the state- spaces are shown in Table5 . Note also that while observing about 8,000 plans executed by the planner in the 3-city logistics domain, the recognizer encounters a case that has already been stored in the library about 1,100 times.... ..."

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### Table 1: Partitioning of boiling water state space.

1993

"... In PAGE 13: ... Figure 8 displays the common three dimensional state space (T; Hw; Hf) for MODELS, and figure 9 illustrates each phase by a shaded region of state space. Table1 provides the formal correspondence of phases and input values with partition blocks. Let (u; p) be the partition block corresponding to the pair (u; p) where u is an input value and p is a phase.... ..."

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### Table 2. Standard state space generation

"... In PAGE 4: ... Set of tasks used for analysis. Task set Tasks set name RG BG S1 Displays and controls 6 4 S2 S1 + built-in test 7 6 S3 S2 + radar control 9 7 S4 S3 + targeting 10 10 S5 S2 + threat response 8 7 S6 S5 + RWR Control 9 8 S7 S6 + weapon control 10 12 S8 S7 + targeting 11 15 Table2 [16] gives the size of the state space for the different sets of tasks listed in Table 1. The Nodes column gives the number of nodes in the state space, and the Arcs column gives the number of arcs in the state space.... ..."

### Table 2. Size of abstract state space

"... In PAGE 6: ... Additional experiments show that more than 100000 trials are necessary to learn a policy on a 204 grid that has equal performance to the policy learned by BASM. From Table2 , we can see that many cells of the regular grids are not necessary to solve the problem. BASM is able to add relatively few but relevant abstract states to the state space.... ..."

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### Table 3: Condensed state space with multiple receivers.

"... In PAGE 14: ... Figure 6 shows the new connection schema for each receiver and its bu ers.By running the TIPP tool we have computed the size of the reduced state spaces for di erent models obtaining the results listed in Table3 . Observing the composition of the equivalence classes given by the strong bisimulation we realised that three di erent kinds of aggregation were captured: the aggregation due to equivalences among old packets and old acknowledges (the same discussed in Section 2.... In PAGE 16: ...ions in all macro-component replicas are the same (i.e. if all receivers work at the same speed and if the server choses the receiver for packet broadcast using a uniform probability distribution) then the aggregation due to symme- try obtained using strong bisimulation is preserved when applying Markovian bisimulation. We end this section by observing that the last line in Table3 shows a result which is not very intuitive: the state space for nrec = mxM = mxP = 3 is smaller that the state space for nrec = 2, mxM = mxP = 3 (9775 and 14025, respectively). This is due to the fact that the sender broadcasts its packets to all the receivers: the addition of a receiver in the system without increasing the network capacity, implies a decrease in the size of the state space since now the sender can broadcast a packet only when the network is empty.... ..."

### Table 2: The state space of the underlying MRGP

"... In PAGE 8: ...ion 4.1.2 (see Figure 5). Details on the analytical solution method can be found in [4]. Table2 , reports the reachability set for the MRSPN of Figure 5, together with useful information for the analysis of the model. The state space is made of 12 tangible states.... In PAGE 8: ... The subsequent regeration period can start from states 1, 10 or 12, and the entering in one of these states is due to some event that makes transition t2 to loose its memory. In particular, as indicated in Table2 , state 1 is reached when transition t2 res (from a state in the subset E). States 10 and 12 form the subset C, and are reached as a consequence of a failure of the processor (token in place p7) which reset the memory of t2 by means of a mra.... ..."

### Table 1: Comparison of state space construction criteria

1996

"... In PAGE 3: ...peaking, they can be categorized into three types, i.e., s Cj Ak a2 jk A1 A2 C1 C2 Set of State Classes a3 a4 beh = lt;s, a, r gt; Action Set Pre-defined (Fixed) Motor Space Behavior Experience Sensor Space Optimize m Figure 3: Classification of behavior experiences B state space construction based on (a) goal/subgoal achievement, (b) obtained reward, and (c) sensor in- put change. Table1 gives a brief comparison of their main features. As can be easily seen from this, each of these criteria has its advantages and disadvantages.... ..."

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### Table 1. Comparison of net sizes (places and transitions) and state spaces (full state space and reduced state space using partial order reduction).

"... In PAGE 17: ... Table1 summarizes the results. For each process, we present the sizes of the resulting nets (in terms of places and transitions) after structural reduction.... ..."

### Table 2. State spaces of the studied models

2002

"... In PAGE 16: ...nents as in [8]. The dimensions of the associated CTMC are shown in Table2 (a); column jSj shows the number of states, and column NZ(Q) gives the number of o -diagonal nonzero matrix entries in Q. For those model con gurations, the implementations of a Jacobi and a Gauss-Seidel solver perform as shown in Table 3(a).... In PAGE 18: ... To obtain a Kronecker representation, we use the same par- tition into four components that was used in [26]. Table2 (b) shows the number of states in the CTMC and the o -diagonal nonzero entries, much like Table 2(a). Table 3(b) gives the computation times we observed on average for a single iteration step for this model.... ..."

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### TABLE II STATE SPACE FOR THE SRN MODELS

2000

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