### TABLE 5. Analysis results. Parameters Reachable nodes Parameters Reachable nodes

1995

"... In PAGE 15: ... Analysis Results The reachability analysis results of the Pr/T-net model in Fig. 7 are shown in TABLE5 . For simplicity we have assumed that all movies have the same duration, which means that the place ACTIVE MOVIES obey the FIFO principle.... In PAGE 15: ...From the TABLE5 it can be seen that the number of users a ects the size of the reachability graph stronger than the number of movies or the number of channels. To be more precise, U users can be put into the FIFO in U! di erent orders.... In PAGE 15: ... Then the number of user combinations possible in the request FIFO is reduced by the factor U!. The sizes of the reachability graphs generated using black user tokens are given in TABLE5... ..."

Cited by 1

### TABLE 5. Analysis results. Parameters Reachable nodes Parameters Reachable nodes

1995

"... In PAGE 15: ... Analysis Results The reachability analysis results of the Pr/T-net model in Fig. 7 are shown in TABLE5 . For simplicity we have assumed that all movies have the same duration, which means that the place ACTIVE MOVIES obey the FIFO principle.... In PAGE 15: ...From the TABLE5 it can be seen that the number of users a ects the size of the reachability graph stronger than the number of movies or the number of channels. To be more precise, U users can be put into the FIFO in U! di erent orders.... In PAGE 15: ... Then the number of user combinations possible in the request FIFO is reduced by the factor U!. The sizes of the reachability graphs generated using black user tokens are given in TABLE5... ..."

Cited by 1

### Table 1. Reachability set of the ABP

"... In PAGE 13: ... As an illustration, consider again the example of the ABP. Starting from the set of reachable con gurations given in Table1 which was computed by the Lcs tool, we generate using the de nition above abstraction functions K and L for the channels K and L. These two functions are equal and coincide exactly with the M uller-Nipkow abstraction function (see Sections 4 and 5).... ..."

### Table 1. Symbolic Interpretation of Reachability Logic

1995

"... In PAGE 11: ...Table 1. Symbolic Interpretation of Reachability Logic To read the rules of Table1 some notation needs to be explained. For D aconstraintsystemandra set of variables (to be reset) r(D) denotes the set of variable assignments fr(v) j v 2 Dg.... In PAGE 12: ...directed graphs (with clock and data variables as nodes), these operations as well as testing for inclusion between constraint systems may be e ectively im- plemented in O(n2)andO(n3) using shortest path algorithms [11, 12, 6]. Now, by applying the proof rules of Table1 in a goal directed manner we obtain an algorithm (see also [13]) for deciding whether a given symbolic network con guration [l;D] satis es a property 93 . To ensure termination (and e ciency), we maintain a (past{) list L of the symbolic network con gurations encountered.... ..."

Cited by 117

### Table 1. Model checking result for Algorithm A with FIFO channels

2004

"... In PAGE 14: ... In PRISM, reachability is performed to identify non-reachable states and the MTBDD is filtered accordingly. Table1 shows statistics for each model we have built. The first part gives the parameters for each model: the ring size n,thesizeofthe identity set, and the size of the channel.... In PAGE 14: ... The second part gives the number of states and transitions in the MTBDD representing the model. Property was successfully checked on all the ring networks in Table1 (we used the model checker PRISM with its default options). Note that for n =4,... ..."

Cited by 4

### Table 1. Model checking result for Algorithm A with FIFO channels

"... In PAGE 11: ... In PRISM, reachability is performed to identify non-reachable states and the MTBDD is filtered accordingly. Table1 shows statistics for each model we have built. The first part gives the parameters for each model: the ring size n, the size of the identity set, and the size of the channel.... In PAGE 12: ... The second part gives the number of states and transitions in the MTBDD representing the model. Property was successfully checked on all the ring networks in Table1 (we used the model checker PRISM 2.0 with its default options).... ..."

### Table 1. Symbolic Interpretation of Reachability Logic

1995

"... In PAGE 9: ...Table 1. Symbolic Interpretation of Reachability Logic To read the rules of Table1 some notation needs to be explained. For D a constraint system and r a set of variables #28to be reset#29 r#28D#29 denotes the set of variable assignments fr#28v#29 j v 2 Dg.... In PAGE 10: ...directed graphs #28with clock and data variables as nodes#29, these operations as well as testing for inclusion between constraint systems may be e#0Bectively im- plemented in O#28n 2 #29andO#28n 3 #29 using shortest path algorithms #5B11, 12, 6#5D. Now, by applying the proof rules of Table1 in a goal directed manner we obtain an algorithm #28see also #5B13#5D#29 for deciding whether a given symbolic network con#0Cguration #5B l; D#5D satis#0Ces a property 93#0C.To ensure termination #28and e#0Eciency#29, we maintain a #28past#7B#29 list L of the symbolic network con#0Cgurations encountered.... ..."

Cited by 9

### Table 1. Reachability Analysis of the Sliding Window Protocol

1998

"... In PAGE 12: ... We only need to check whether one of the three rst conditions in the proof of Lemma 7 holds. 8 Example In this section we apply our algorithm ( Table1 ) to a sliding window protocol (shown in Figure 1). We use a symbolic representation of the form hsi; qj; r1; r2i, where si and qj are the control states of the sender and the receiver, respec- tively, and r1 and r2 are SREs which describe the contents of the message and acknowledgement channels.... ..."

Cited by 60

### Table 1. Reachability Analysis of the Sliding Window Protocol

1998

"... In PAGE 10: ... We only need to check whether one of the three rst conditions in the proof of Lemma 7 holds. 8 Example In this section we apply our algorithm ( Table1 ) to a sliding window protocol (shown in Figure 1). We use a symbolic representation of the form hsi; qj; r1; r2i, where si and qj are the control states of the sender and the receiver, respectively, and r1 and r2 are SREs which describe the contents of the message and acknowledgement channels.... ..."

Cited by 60

### Table 3: Commands for backward reachability analysis.

"... In PAGE 13: ...Table 3: Commands for backward reachability analysis. Table3 lists the commands for predecessor operator and backward reachability analysis. The command pre exactly calculates the one step backward reachable set for uncertain piecewise linear systems.... ..."