### Table1. Definition of the rewritings of the disjunctive predicates.

"... In PAGE 7: ... We consider four rewritings, each one deserving a particular decision coverage criterion. Table1 distinguishes these rewritings. It consists in creating a bounded choice ([]) between the different elements of the rewriting, expanding the control... ..."

### Table 3. Lazy compilation for several kinds of disjunctions.

2005

"... In PAGE 12: ...2 Evaluation In the first experiment, we will measure the overhead of the new lazy compilation scheme. The artificial queries from Table3 have no unreachable parts, and as such provide a worst case for lazy compilation overhead. In practical applications, we expect the queries to have unreachable parts, and so the total overhead of the lazy compilation scheme will be compensated by the smaller compilation time.... In PAGE 12: ... In practical applications, we expect the queries to have unreachable parts, and so the total overhead of the lazy compilation scheme will be compensated by the smaller compilation time. The experiments of Table3 use only the first two benchmarks from Table 1. The other benchmarks of Table 1 yield similar results.... In PAGE 15: ... The timings show that, for our benchmarks, the compilation time in compile amp; run is systematically larger than the execution time for all the examples such that the impact of improving the compilation has a larger effect on the total times. Table3 shows that lazy compilation has some overhead, but we hoped that it would be compensated by avoiding the compilation of failing parts in the query packs. This is indeed the case for all datasets.... ..."

### Table 1. Median cycles for the Synchronous Branch and Bound for nding an optimal

1997

"... In PAGE 13: ... Also note that the initial value of 8iN i was set to the value of the maximum degree of a constraint graph minus one, and that of 8iS i was zero. Table1 illustrates the median cycle for nding an optimal solution and the mean optimal distance over 25 instances for each class. The cost of nding an optimal solution by SBB clearly seems to be very high.... ..."

Cited by 39

### Table 1: SDP approximation for EQP by iteratively adding sign constraints. The number and largest violation of sign constraints are displayed together with computation time and the lower bound.

1997

"... In PAGE 11: ... Solve the SDP min 1 2L X such that diag(X) = e; Xe = me; X 0; and iteratively add only a few of the most violated sign constraints xij 0. Table1 contains some results using this approach. We note for instance that in the case of partitioning into k = 10 subsets, the initial lower bound of 275.... In PAGE 11: ... The value of the best feasible solution found is given in the column labeled `cut apos;. The computational behavior shown in Table1 is quite typical for SDP relaxations of combinatorial optimization problems. Most of the improvement is obtained in the rst few iterations.... ..."

Cited by 76

### Table 1: The di erent types of optimization problems treated in NLPLIB TB. probType Number Description of the type of problem uc 1 Unconstrained optimization (incl. bound constraints). qp 2 Quadratic programming.

1999

"... In PAGE 3: ... The global variable probType is the current type to be solved. An optimization solver is de ned to be of type solvType, where solvType is any of the probType entries in Table1 . It is clear that a solver of a certain solvType is able to solve a problem de ned to be of another type.... In PAGE 19: ...65 Table1 0: Information stored in the structure Prob.NTS Field Description SepAlg If SepAlg = 1, use separable non linear least squares formulation, default 0.... In PAGE 19: ... alpha Weights in autoregressive models. Table1 1: Information stored in the structure Prob.PartSep Field Description pSepFunc Number of partially separable functions.... In PAGE 20: ...66 Table1 2: Information stored in the structure Prob.GLOBAL Field Description iterations Number of iterations, default 50.... In PAGE 20: ... t t(i) is the total number of splits along dimension i. Table1 3: Information stored in the structure Prob.USER Field Description f Name of m- le computing the objective function f(x).... In PAGE 21: ...67 Table1 4: Information stored in the structure Prob.optParam.... In PAGE 22: ...68 Table1 5: Information stored in the global Matlab structure Result. Field Description Iter Number of major iterations.... In PAGE 23: ...69 Table1 6: The state variable xState for the variable. Value Description 0 A free variable.... In PAGE 23: ... 3 Variable is xed, lower bound is equal to upper bound. Table1 7: The state variable bState for each linear constraint. Value Description 0 Inactive constraint.... In PAGE 23: ... 3 Linear equality constraint. Table1 8: Information stored in the structure Result.GLOBAL Field Description C Matrix with all rectangle centerpoints in original coordinates.... In PAGE 23: ... t t(i) is the total number of splits along dimension i. Table1 9: Matlab Optimization toolbox routines with a TOMLAB interface. Function Type of problem solved constr Constrained minimization.... ..."

Cited by 3

### Table 1 Constraint bounds for platform.

### Table 3. Design Objective Function Results

1997

"... In PAGE 7: ...hrust (Fig. 10) slightly, approximately 0.1 percent, which resulted in a reduction in nozzle weight. The final results for each case and the initial value of the objectives and the design parameters are given in Table3 and Table 4, respectively. Note that significant changes in the design variables are observed between the single-discipline optimized solution and the MDO with eight variables that vary by more than 5 percent.... ..."

Cited by 4

### Table 1 The di erent types of optimization problems treated in TOMLAB. probType Number Description of the type of problem uc 1 Unconstrained optimization (incl. bound constraints). qp 2 Quadratic programming.

"... In PAGE 3: ...rowing. This motivates a well-de ned naming convention and design. TOMLAB solves a number of di erent types of optimization problems. Currently, we have de ned the types listed in Table1 . The global variable prob- Type is the current type to be solved.... In PAGE 3: ... The global variable prob- Type is the current type to be solved. An optimization solver is de ned to be of type solvType, where solvType is any of the probType entries in Table1 . It is clear that a solver of a certain solvType is able to solve a problem de ned to be of... ..."

### Table 3. (Taken from [104, 106]) Complexity of Disjunctive Logic Programs (with Integrity Constraints)

### Table 1. Comparison of number of results for latex software query. Search tool/ Disjunctive Conjunctive Phrase

1997

"... In PAGE 7: ... The first query was intended to find both public-domain sources and commercial vendors for obtaining LaTex software, whereas the second query was intended to locate relevant research publications on multiagent system architecture. Table1 presents results for the first query. The second col- umn indicates the number of documents retrieved by inter- preting the query as a disjunction of the query terms.... ..."

Cited by 25