### Table 1: Four protein backbones modeled by open polygonal knots. The size of the problem is measure by the number of edges, a2 , and the number of crossings in the chosen projection, a0 . The time the sweep-line (a1a9a2a5a4 ), the approximate double-sum (a6a11a1 a8

"... In PAGE 8: ... Fig- ure 11 displays the four backbones chosen for our experi- mental study. Table1 presents some of our findings. Thick knots.... ..."

### Table 2: Time needed to solve the n queens problem on a 700 MHz In- tel Pentium III system.

"... In PAGE 38: ... We explored the net with some Petri net tools, and we also solved the problem with the CSPLIB [154] implemen- tation of the FC-CBJ algorithm. For the Petri net tools, the execution times reported in Table2 exclude the time needed by code generators. The main reason why FC-CBJ outperforms the Petri net tools in this example is that it allocates look-up tables of infeasible solutions [134, Section 6].... In PAGE 39: ... Unfortunately, we were unable to measure the performance of this package, because it does not support exhaustive state space enumeration, only random simulation. In Table2 , the proportional speed difference between Design/CPN and other Petri net tools seems to grow with the size of the problem. Thus, it cannot be solely explained by the choice of implementation lan- guage.... In PAGE 42: ...ysis methods, such as the sweep-line method [99, 100]. The choice of implementation language could be one reason why Table2 suggests that Design/CPN consumes more resources than other high-level net tools. Prod [155] is one of the best-known model checker tools for high- level nets.... ..."

Cited by 1

### Table 2: Time needed to solve the n queens problem on a 700 MHz In- tel Pentium III system.

"... In PAGE 36: ... We explored the net with some Petri net tools, and we also solved the problem with the CSPLIB [154] implemen- tation of the FC-CBJ algorithm. For the Petri net tools, the execution times reported in Table2 exclude the time needed by code generators. The main reason why FC-CBJ outperforms the Petri net tools in this example is that it allocates look-up tables of infeasible solutions [134, Section 6].... In PAGE 37: ... Unfortunately, we were unable to measure the performance of this package, because it does not support exhaustive state space enumeration, only random simulation. In Table2 , the proportional speed difference between Design/CPN and other Petri net tools seems to grow with the size of the problem. Thus, it cannot be solely explained by the choice of implementation lan- guage.... In PAGE 40: ...ysis methods, such as the sweep-line method [99, 100]. The choice of implementation language could be one reason why Table2 suggests that Design/CPN consumes more resources than other high-level net tools. Prod [155] is one of the best-known model checker tools for high- level nets.... ..."

### Table 2: Time needed to solve the n queens problem on a 700 MHz In- tel Pentium III system.

"... In PAGE 38: ... We explored the net with some Petri net tools, and we also solved the problem with the CSPLIB [154] implemen- tation of the FC-CBJ algorithm. For the Petri net tools, the execution times reported in Table2 exclude the time needed by code generators. The main reason why FC-CBJ outperforms the Petri net tools in this example is that it allocates look-up tables of infeasible solutions [134, Section 6].... In PAGE 39: ... Unfortunately, we were unable to measure the performance of this package, because it does not support exhaustive state space enumeration, only random simulation. In Table2 , the proportional speed difference between Design/CPN and other Petri net tools seems to grow with the size of the problem. Thus, it cannot be solely explained by the choice of implementation lan- guage.... In PAGE 42: ...ysis methods, such as the sweep-line method [99, 100]. The choice of implementation language could be one reason why Table2 suggests that Design/CPN consumes more resources than other high-level net tools. Prod [155] is one of the best-known model checker tools for high- level nets.... ..."

### 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.... ..."

### Table 1: Spin statistics: state space generation + model checking

"... In PAGE 24: ... Whenever an error was found, we reran the veri cation with a smaller search depth (option `-m apos; at run time) to see if a smaller error trail could be found. In this way we found the trails reported in Table1 , which are the shortest trails we could nd. Sometimes the search for a shorter trail involves the exploration or more states and transitions, due to the order in which the depth- rst search is performed.... In PAGE 27: ... However, the possibility to track invalid end states was a simple way around this, although it implied changing the models. Performance of Spin As can be seen in Table1 , the performance of Spin is quite good, as long as the number of DCM Managers remains small, and there are no asynchronous channels. We achieved the best performance by using all the advice given in Spin apos;s Help Section on reducing the state space size.... ..."

### Table 3. Summary of 2-way direction join algorithms sweep line range search data

2001

"... In PAGE 9: ... If the evaluation needs only 1-dimensional range searches, B-trees are su cient for the temporary data structure. Column 4 of Table3 shows the data structures used in the evaluation of a direction join. Theorem 3.... ..."

Cited by 3

### Table 1. Completely exploring state spaces with BFS and several reduction methods. marriers(3)

"... In PAGE 8: ... The main question to investigate is therefore how C2o performs in comparison to C2s. Table1 depicts results obtained by exploring the state space of some models, where a depth bound is imposed in those cases where an exhaustive exploration is not feasible within a... In PAGE 9: ... For the remaining models both provisos either work equally well, or C2o prevails. By comparing the two previous sets of experiments we observe the following phenomenon: in the marriers model, algorithm BFS with C2o explores as many states as BFS with C2i ( Table1 ), while A* with C2o explores almost twice as many states as A* with C2i (Table 2). In other words, the C2o proviso is refuting ample sets when the search algorithm is A* but not when it is BFS.... ..."

### Table 1. Completely exploring state spaces with BFS and several reduction methods. marriers(3)

"... In PAGE 8: ... The main question to investigate is therefore how C2o performs in comparison to C2s. Table1 depicts results obtained by exploring the state space of some models, where a depth bound is imposed in those cases where an exhaustive exploration is not feasible within a memory bound of 512 MB. The exploration is performed using BFS as search algorithm in combination with vari- ous reduction methods: no partial-order reduction at all (no), no action ignoring prevention (C2i), and the pro- visos C2v, C2s and C2o.... In PAGE 9: ... For the remaining models both provisos either work equally well, or C2o prevails. By comparing the two previous sets of experiments we observe the following phenomenon: in the marriers model, algorithm BFS with C2o explores as many states as BFS with C2i ( Table1 ), while A* with C2o explores almost twice as many states as A* with C2i (Table 2). In other words, the C2o proviso is refuting ample sets when the search algorithm is A* but not when it is BFS.... ..."