### Table 2. Overview on the probabilities computed for the properties MDOL and BDOL for di erent time bounds, for main and backup disk load = 10.

2005

"... In PAGE 12: ... In order to preserve all probabilistic information of the model, the remainder of the model is replaced by a special absorbing state sout to which we redirect all transitions which originate from some state on the path to the goal states, but which are not part of the path. Table2 shows an overview on the probabilities computed for the properties MDOL and BDOL. In order to assess the quality of some counterexample that we found we compare the reachability probability of the counterexamples with the precise reachability probability of the property in the original model, as determined by a transient analyser.... In PAGE 13: ... Overview on the probabilities computed for the properties MDOL and BDOL for di erent time bounds, for main and backup disk load = 10. are recorded in Table2 , namely the estimated and the precise ones, c.f.... ..."

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### Table 3. Results for checking P2 using symC for different time bounds.

2004

"... In PAGE 23: ... Thus, the comparison with the SystemC approach does not completely match. As we see in Table3 , we can also check the property with symC, however we get complete coverage within this range. For model M3, symC even beats the combined SystemC and RAVEN approach.... ..."

Cited by 3

### Table 1. Time bounds.

"... In PAGE 1: ... The deterministic solution is essentially a derandomization of the randomized solution. Table1 lists the time bounds for the mth operation in a sequence of operations. The incremental space cost is given in Table 2.... ..."

### Table 1. Time bounds for different solutions to the Time Queue problem

"... In PAGE 3: ... The standard heap described by Williams [18] can be modified to use fingers by adding a dictionary that stores the position in the heap for each element. The heap solution (heap in Table1 ) even works if the maximum duration is unbounded and it only needs O(N) space. The model used is the pointer machine model [11].... In PAGE 3: ...) [13,15]. However, the stratified tree needs O(C + N) space. The model is the pointer machine model. Willard shows how perfect hashing (see [6, 8]) can be used to improve the space bound to O(N) for the stratified tree [17] (vEB-W in Table1 ). The model is the RAM model [14] of the stronger cell probe model [19] due to the hashing.... In PAGE 3: ... They use O(C + N) space in the Yggdrasil implementation [2] of the RAMBO model [9]. So far we have seen the bounds in Table1 , with the Calendar queue (CQ)... ..."

### Table 1: Results of symbolic evaluation of time-bound functions (exact counts).

2002

"... In PAGE 10: ... The example programs shown here are: ack: Ackermann function programmed using the standard rst- order recursive de nition; ack-curried: a curried version of Ackermann function that uses higher-order functions (and is almost twice as fast as the standard rst-order function); tak-cps: the Takeuchi function in CPS, part of the Gabriel benchmark suite [14]; reverse: standard rst-order list reverse function; rev-cps: a CPS version of reverse; split: taking a predicate and a list and returning two lists, one whose elements satisfy the predicate and another whose elements do not satisfy the predicate; x: factorial function programmed using the Y combinator for a heavy use of higher-order functions; map: standard map function; union: taking two sets and returning the union; index: taking an item and a list and returning the index of the item in the list, or ?1 if the item is not in the list. Table1 gives the results of symbolic evaluation of the time-bound functions for these example programs on inputs of various sizes. Several counts of the primitive operations are merged to t the table on the page.... ..."

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### Table 3: Comparison of solution quality of search with and without abstraction. Time-bound

1992

"... In PAGE 14: ...sed. For the search without abstraction, the latter vector is the one used as constraints. Recall that by this vector the constraints C n and C d are considered more important than the constraint C l . Table3 describes the comparisons in the quality of solutions found, taking both sets of constraints as soft ones, and giving both problem-solvers an equal time bound (18 CPU seconds on a Sun4 Sparc Station). Each item in the table is a vector (x;; y), where x is the number of remaining violations with the most important constraint, and y the least important one.... ..."

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### Table 1). The dotted lines give the average gains without the use of problem sizes, and the solid lines are for the gains with the regression. The graphs show that the use of sizes usually, though not always, leads to a small improvement. The apparent advantage of the regression in delay apos;s learning is mostly due to the choice of low time bounds for problems 9 and 10, which cannot be solved in feasible time. This luck in setting low bounds for two hard problems is not statistically signi cant. If the algorithm does not use problem sizes, it hits the time bounds of 16.9 and 14.0 on these problems (see Figure 5) and falls behind in its per-problem gain.

1997

"... In PAGE 3: ... The application of a method to a problem gives one of three outcomes: it may solve the problem; it may terminate with failure, after exhausting the available search space without nding a solution; or we may interrupt it, if it reaches some pre-set time bound without termination. In Table1 , we give the results of solving thirty transportation problems, by each of the three methods; we denote successes by s, failures by f, and hitting the time bound by b.... In PAGE 4: ...1 s 5.4 f 4 Table1 : Performance of apply, delay, and alpine on thirty transportation problems. Note that these data are only for illustrating the selection problem, and not for a general comparison of these search techniques; their relative performance may be very di erent in other domains.... In PAGE 4: ... Also note that the selection technique does not rely on speci c properties of prodigy; it is equally applicable to selection among multiple methods in any AI system. Although each method outperforms the others on at least one problem (see Table1 ), a glance at the data reveals that apply apos;s performance in this domain is probably the best among the three. We use statistical analysis to con rm this intuitive conclusion, and show how to choose a time bound for the selected method.... In PAGE 12: ...pply apos;s estimate of the maximal-gain bound, after solving all problems, is 9.6. It di ers from the 11.6 bound, found from Table1 , because the use of bounds that ensure a near-maximal gain has prevented su cient exploration. delay apos;s total gain is 115.... In PAGE 12: ...elay apos;s total gain is 115.7, or 3.9 per problem. If we used the data in Table1 to nd the optimal bound, which is 6.2, and solved all problems with this bound, we would earn 5.... In PAGE 12: ...3 per problem. The estimate based on Table1 gives the bound 11.0, which would result in earning 12.... In PAGE 14: ...0. In this experi- ment, we rst use the thirty problems from Table1 and then sixty additional transportation problems. The horizontal axis shows the number of a problem, and the vertical axis is the running time; we mark successes by circles and failures by pluses.... In PAGE 19: ... We denote the number of sample problems by n, the problem sizes by size1; :::; sizen, and the corresponding running times by time1; :::; timen. In Figure 12, we give the results of regressing the success times for the transportation problems from Table1 . The top three graphs show the polynomial dependency, whereas the bottom graphs are for the exponential dependency.... In PAGE 20: ... We also allow the user to set a regression slope, which is useful when the past data are not su cient for an accurate estimate. If the user speci es a slope, the system uses her value in the regression; however, it compares the user apos;s value with the regression estimate of Table1 1, determines the statistical signi cance of the di erence, and gives a warning if the user apos;s estimate is o with high probability. Note that the least-square regression and related t-test make quite strong assumptions... ..."

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### Table 20: Comparable time bounds for alternative 1, data copying methods

"... In PAGE 50: ... The measured values in Table 17 are used to calculate the probable transmission time. In Table20 , these calculated values are shown. The values in the table are calculated applying the simplified model in Equation 2.... In PAGE 50: ...Table 20: Comparable time bounds for alternative 1, data copying methods Please notice that the values in Table20 are not calculated with consideration to the requirement of the switching capacity. Those values are only used to compare the methods for solving this sub-domain.... In PAGE 51: ... If alternative 1, namely copying the data directly from the slave memory, is used it will take 1.76 seconds to perform the data copying part of the program, see Table20 . If the slave memory is copied via the VME memory instead, it will take 1.... ..."

### Table 1: Random MPE. Time bound 30 sec. 100 samples.

1999

"... In PAGE 4: ... Each entry in the table reports the number of instances that fall in a speci c range of accuracy, as well as the average running time of each algorithm (note that BBMB time includes the preprocessing time by MB). For example, Table1 reports the results with random problems having N=256, K=2, P=2. There are 5 hori- zontal blocks, each corresponding to a di erent value of C.... In PAGE 4: ... The rest of the columns present results of MB and BBMB for various values of the bound i. Looking at the rst line in Table1 we see that in the best ac- curacy range, opt 0:95, MB with i = 2 solved only 14 problems using 0.03 seconds on the average.... ..."

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### Table 1. Thus, the minimal XL-Like Attack time bounds are roughly concordant with that of Dual Rank Attack time bounds.

"... In PAGE 3: ...0 0.60 Table1 : Security and Performance of Enhanced TTS, B4D1BN D2B5 BP hash and signature sizes As seen in Table 1 (speed tests on a 500 MHz Pentium III PC with gcc3), compared to RSA, the patched TTS variant has good security2 levels against known attacks, and it signs 3 orders of magnitude faster (cf.... In PAGE 3: ...0 0.60 Table 1: Security and Performance of Enhanced TTS, B4D1BN D2B5 BP hash and signature sizes As seen in Table1 (speed tests on a 500 MHz Pentium III PC with gcc3), compared to RSA, the patched TTS variant has good security2 levels against known attacks, and it signs 3 orders of magnitude faster (cf.... In PAGE 12: ... This is related to the CSCXD1 C0BD parameter of the central equations. For now see Table1 for estimated security levels for conformant tame-like schemes under XL.... ..."