### Table 1. DIMACS unsatisfiable instances. Time in seconds. A - means the problem was not solved in less than 600 seconds.

2003

"... In PAGE 9: ... 4.2 Results The results for DIMACS benchmarks are shown in Table1 and 2. For each instance, the table lists the instance name, the number of variables (|V |), the number of clauses (|C|), the optimum (minimization of the clause violation), and the total cpu time in seconds (rounded downwards) for the various solvers.... In PAGE 9: ... Note that all these problems have an extremely low optimum value, which means that they are near the transition peak. As observed by [27], these instances are hard as SAT instances but easy as Max-SAT instances (the hardest instances have higher clauses to variables ratio which causes high optimum values) In Table1 , MFDAC was able to solve almost half of the instances while PBS solved them all. We do not report larger instances (|V | gt; 100) where PBS was the only successful algorithm (except for CPLEX on hole10).... ..."

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### Table 1. Number of recursions recur, number of assignments assign, and computation time time required for solving (unsatisfiable) Equation (4).

### Table 3: Unsatisfiable problems that respectively take at least 3, 20, and 100 applications of Backjump without lemmas within 300s, where Solved Problems gives the number of problems solved by a configuration, while the remaining values are for the subsets of 561, 191, 89, and 61 problems solved by all configurations.

in Abstract

2006

"... In PAGE 22: ... Since experimental results for unsatisfiable problems are usually more stable with respect to different space exploration orders, it is instructive to separate the data in Table 2 between unsatisfiable and satisfiable problems. These data are provided respectively in Table3 and Table 4. The separated results for unsatisfiable and satisfiable problems show the same pat- tern as the aggregate results in Table 2.... ..."

### Table 11. Enumeration of most complex Boolean functions by hexadecimal function vectors

"... In PAGE 19: ...277 Table11 enumerates all most complex Boolean functions depending on k = 1,.... In PAGE 19: ...,...,4 variables. The content of this Table was calculated using the algorithm 4. It can be seen in Table11 that the root of all most complex functions are the trivial functions f1(x) = x, f2(x) = x, and f3(x) = 1. Using the recursive algorithm 4 any most complex Boolean function can be calculated very quickly.... ..."

### Table 1: DIMACS benchmarks subset.

2003

"... In PAGE 4: ... 5 Comparison of branching rules In [17], a detailed comparison between the branching rules mentioned above is presented. To validate these results we performed experiments for the same set of DIMACS benchmarks (see Table1 ) on a AMD Athlon(TM) XP1700+, restricted to 512MB main memory and 180sec of CPU runtime for each instance. Each class of the benchmark set consists of several instances1 which can be either satisfiable (see column #SAT) or unsatisfiable (see column #UNSAT).... In PAGE 8: ... Since there are several possibilities for choosing a pref- erence value initialization (3x), branching rule selection method (3x) and difference distribution mech- anism (2x) we have conducted experiments with B4BF A1 BF A1 BEB5 BP BDBK configurations. Since our approach is a randomized method (namely the application of the proposed selection methods), we handled each in- stance of the benchmark set (see Table1 ) 30 times for each of the 18 parameter settings. All experiments were performed on a AMD Athlon(TM) XP1700+, restricted to 512MB main memory and 180sec of CPU runtime for each instance.... ..."

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### Table 1: DIMACS benchmarks subset.

2003

"... In PAGE 4: ... 5 Comparison of branching rules In [17], a detailed comparison between the branching rules mentioned above is presented. To validate these results we performed experiments for the same set of DIMACS benchmarks (see Table1 ) on a AMD Athlon(TM) XP1700+, restricted to 512MB main memory and 180sec of CPU runtime for each instance. Each class of the benchmark set consists of several instances1 which can be either satisfiable (see column #SAT) or unsatisfiable (see column #UNSAT).... In PAGE 8: ... Since there are several possibilities for choosing a pref- erence value initialization (3x), branching rule selection method (3x) and difference distribution mech- anism (2x) we have conducted experiments with B4BF A1 BF A1 BEB5 BP BDBK configurations. Since our approach is a randomized method (namely the application of the proposed selection methods), we handled each in- stance of the benchmark set (see Table1 ) 30 times for each of the 18 parameter settings. All experiments were performed on a AMD Athlon(TM) XP1700+, restricted to 512MB main memory and 180sec of CPU runtime for each instance.... ..."

Cited by 1

### Table 2: Enumeration of the elements of

1997

"... In PAGE 18: ... We list examples for powers of two up to 64 below: We then start with the element , and enumerate all non-zero polynomials over by multiplying the last element by , and taking the result modulo . This is done in Table2 below for , where . It should be clear now how the C code in Figure 4 generates the gflog and gfilog arrays for , and .... ..."

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### Table 1. Enumeration of Toroidal Polyhexesa

"... In PAGE 3: ... The dual of a toroidal polyhedral polyhex is a triangulation of the torus. To illustrate the relationship of the various definitions, we give the counts for small cases in Table1 , using data extracted from the papers of Negami15 and Altschuler.16 The tabulations given by Kirby10,12 include some nonpolyhedral cases.... ..."

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### Table 1 Results of enumeration

2002

"... In PAGE 4: ...#teams: the number of teams (2N), #equitable: the number of equitable HATs (?2N?2 N ), #o amp;c: the number of equitable HATs satisfying opening and closing conditions (?2N?4 N ), #triple: the number of equitable HATs satisfying opening and closing conditions and a triple break constraint. Table1 shows that a triple break constraint drastically decreases the number of the candidates. The compu- tational time for enumerating all the HATs appearing in Table 1 is less than 1 second on Windows 98 PC (CPU: AMD Athlon 950MHz, RAM: 640MB).... In PAGE 4: ... Table 1 shows that a triple break constraint drastically decreases the number of the candidates. The compu- tational time for enumerating all the HATs appearing in Table1 is less than 1 second on Windows 98 PC (CPU: AMD Athlon 950MHz, RAM: 640MB). Then we solved the integer programming problems for checking the feasibility of the remaining HATs.... ..."

### Table 4: Scores on Subset of TIDES 2003 Dataset

2005

"... In PAGE 9: ...5440 MEMT System .5347 Table 3: Scores on Full TIDES 2003 Dataset Table4 shows the METEOR scores for the three online translators, the oracle system that chose the best original translation, MEMT, and the ora- cle system which chose the best hypothesis generated by MEMT on the subset of the 2003 TIDES dataset that was used for the oracle ex- periment. It is interesting to note that the second online translator performed worse while all the other systems performed better on this sample of the test set.... ..."

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