### Table 7 addresses problems of the same size as in Table 6, but for which the optimal values are unbounded. For all these instances, only the forbiddance problem (FU) is solved. Moreover, the solution process stops as soon as a feasible solution with a positive value is obtained.

2001

"... In PAGE 26: ...mx = mu = 100, quot;x = quot;u = :1 and = 15 Table7 : Detection of unboundedness by CBA (X bounded and U unbounded) All 70 instances considered in Table 7 are quickly solved, and only 2 of them required the BB part of the algorithm, C4 criterion being reached for these two problems.... In PAGE 26: ...mx = mu = 100, quot;x = quot;u = :1 and = 15 Table 7: Detection of unboundedness by CBA (X bounded and U unbounded) All 70 instances considered in Table7 are quickly solved, and only 2 of them required the BB part of the algorithm, C4 criterion being reached for these two problems.... ..."

Cited by 1

### Table V (c) summarizes the average running time (in seconds) for the three methods across all 84 test cases (for R-bound/L-unbound). Pre-processing time is not included. For example, for CS, the SES surface and context shapes are computed off-line. Likewise, the time to calculate the SES for PatchDock, and surface residues for ZDOCK, is also not included. We find that on average, PatchDock is the fastest approach. It is about 2 times faster than CS. On the other hand CS is about 1.5 times faster than ZDOCK(PSC).

### Table 5 Unbound Examples.

"... In PAGE 13: ... This gave us a possibility to compare our results with the real-life solution. Table5 lists the names of the docked proteins as well as their crystal resolution. The examples were chosen as large proteins (see Table 6), that have been crystallized both in complex and as separate molecules (unbound proteins).... ..."

### Table 1: Comparison of known adaptive algorithms. In this table, k denotes point contention, kprime denotes interval contention, and M denotes an upper bound on the maximum number of processes concurrently active in the system (possibly less than N). (Although [2] uses a bounded number of variables, some of these variables are unbounded.) Each algorithm has bounded RMR time complexity on CC machines with write-update caches. Since these algorithms are quite complicated, it is unclear whether they are adaptive on CC machines in general.

2000

Cited by 30

### Table 1 contains the results for the application of the H* ordering. This table contains: the transversal bound, , which was found by H0; the total time for the H* ordering (user process time in seconds) on one processor of Cedar; the total number of diagonal blocks after the ordering; the number of rows in the border; and the order of the largest diagonal block. The use of an unbounded transversal is indicated in Table 1 by a * in the bound column.

1996

Cited by 16

### Table 1: A comparison of N-process k-exclusion algorithms for shared-memory systems. Time complexity is measured in terms of the number of remote memory references. Therefore, algorithms that do not spin locally have unbounded time complexity. In the rst column of time complexity gures, c is the level of contention. The compare-and-swap- based algorithms of Theorems 11 and Theorem 12 improve upon the algorithms of Theorems 7 and 8 by having lower space complexity.

"... In PAGE 2: ... The renaming algorithm we present is based on test-and-set, and has time complexity that is directly proportional to the number of processes that concurrently hold or request names. Table1 compares the k-exclusion algorithms presented in this paper to previously known ones. This table gives the time complexity (see below) of each listed algorithm, both under contention and in the absence of contention.... In PAGE 2: ...his usage is consistent with the notion of contention for the implemented object (i.e., the number of processes that concurrently access the object). Table1 also speci es the set of instructions used by each algorithm, and whether or not the algorithm is starvation-free. Time complexity gures in the table specify the number of remote accesses of shared memory required per critical section acquisition.... In PAGE 2: ... Hence, they can be implemented on distributed shared-memory machines that do not have coherent caches. For both classes of machines, we present algorithms that have O(k log(N=k)) time complexity under contention and algorithms that have time complexity that is directly proportional to contention (see Table1 ). As shown in Table 1, all of these algorithms have constant time complexity in the absence of contention, and are based on commonly-available 1The k-assignment problem was originally posed by Attiya et al.... ..."

### Table 5. Performance of unbounded verification

"... In PAGE 24: ...3 Unbounded verification and attack discovery performance In this last part we present in Table 4 a comparison of the efficiency of finding an attack by the six tools on Needham-Schroeder, for the secrecy properties. Next, we present for the tools which are able to verify protocols for an unbounded number of runs, a comparison of their efficiency for the unbounded verification of correctness of the protocol in Table5... In PAGE 25: ... This includes Scyther, ProVerif and TA4SP, where we have considered only the secrecy properties. We perform this analysis on the four selected pro- tocols, and detail the results in Table5 . With respect to the used notation, we mention that 0.... ..."

### Table 2. Finite and Unbounded Models.

1996

"... In PAGE 4: ...Table2... ..."

Cited by 1

### Table 3: Algorithm to Instantiate Variable.

"... In PAGE 4: ... Since total-time is always as- sumed to be unbounded the process yields the inter- val [24; 94] for the street-* variables and [1; 97] for all avenue-*-variables. Instantiating Variables as depicted in Table3 ne- glects preconditions and computes a flxpoint for the variable domains by considering the numerical efiects in the operator set only. Similar to fact space ex- ploration we utilize a queue Q, containing possible variable-value pairs.... ..."

### Table 2: RSP for Unbounded Start Delay.

1995

"... In PAGE 3: ... This principle was introduced in [4] and has proven to be very useful in system verifications. Specialised to the recursive equation defining the unbounded start delay, RSP instantiates as shown in Table2 . This special form of RSP will be called RSP(USD) in... ..."

Cited by 2