### Table 2. An example of constraint solving on sets of integers

"... In PAGE 14: ... For example, fS;; S1:: 0 Set Int;; S 2 [f1g;; f1;; 2;; 3;; 4g];;S1 2 [f3g;; f1;; 2;; 3g];; S 0 S1g produces the re ned domains S 2 [f1g;; f1;; 2;; 3g]andS1 2 [f1;; 3g;; f1;; 2;; 3g]. Table2 details the process fol- lowed. The constraints are labeled as c1;;c2;;c3;;c4andc5 respectively and trans- lated to the following triples: (c1) (:: 0 ;; fSg;; fS 2 [? Set Int ;; gt; Set Int ]g) (c2) (:: 0 ;; fS1g;; fS1 2 [? Set Int ;; gt; Set Int ]g) (c3) (2;; fSg;; fS 2 [f1g;; f1;; 2;; 3;; 4g]g) (c4) (2;; fS1g;; fS1 2 [f3g;; f1;; 2;; 3g]g) (c5) ( 0 ;; fS;; S1g;; fS 2 [? Set Int ;;max(S1)];;S1 2 [min(S);; gt; Set Int ]g) Table 2.... ..."

### Table 2. An example of constraint solving on sets of integers C

1998

"... In PAGE 14: ... For example, fS; S1::0 Set Int; S 2 [f1g; f1; 2; 3; 4g]; S1 2 [f3g; f1; 2; 3g]; S 0 S1g produces the re ned domains S 2 [f1g; f1; 2; 3g] and S1 2 [f1; 3g; f1; 2; 3g]. Table2 details the process fol- lowed. The constraints are labeled as c1; c2; c3; c4 and c5 respectively and trans- lated to the following triples: (c1) (::0; fSg; fS 2 [?Set Int; gt;Set Int]g) (c2) (::0; fS1g; fS1 2 [?Set Int; gt;Set Int]g) (c3) (2; fSg; fS 2 [f1g; f1; 2; 3; 4g]g) (c4) (2; fS1g; fS1 2 [f3g; f1; 2; 3g]g) (c5) ( 0; fS; S1g; fS 2 [?Set Int; max(S1)];S1 2 [min(S); gt;Set Int]g) Table 2.... ..."

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### Table 6: An example of constraint solving on sets of integers C

### Table 6: An example of constraint solving on sets of integers C

### Table I. Table I: Problem sizes of deterministic equivalents. Formulation Scenarios Constraints Variables Integers Multipliers

in A Two-Stage Stochastic Program for Unit Commitment Under Uncertainty in a Hydro-Thermal Power System

1998

Cited by 10

### Table 1. Experimental results for performance of di erent encodings of integer arithmetic constraints within the disjunctive composite representation. Time measurements appear in seconds.

### Table 1: The size of the formulated 0-1 integer programming problem. # of nodes # of variables # of inequality constraints

"... In PAGE 8: ... (Note that each variable corresponds to a node group, while each inequality constraint corresponds to a partition of V .) Table1 shows the size of the 0-1 integer programming problem for networks of up to 12 nodes. The number of variables is the same as that of node groups, i.... In PAGE 13: ... In the case of Network 7, for example, the number of variables is 219 and that of inequalities is 1519. Comparing these values with Table1 , one can see that the number of variables is reduced by half and that of the inequality constraints is decreased by more than 90%. (Notice that Network 7 has nine nodes.... ..."

### Table 2. Experimental results for performance of di erent automata-based encodings of integer arithmetic constraints and boolean formulas. Time mea- surements appear in seconds.

"... In PAGE 16: ...7. In Table2 , we show the types and the number of xpoint iterations (F denotes the forward xpoint com- putation, EG and EF denote the xpoint computations for corresponding CTL operators), and the number of integer and boolean variables for each problem in- stance. For each version of the veri er we recorded the following statistics: 1) Time... ..."

### Table 6: Variables and constraints for the action fly of the application example. We have used integer domains because real variables are still under development in Choco.

"... In PAGE 7: ... The input plan, with the durations of each action and the basic causal links, is shown in Figure 3. This plan is then formulated via constraint programming as shown in Table6 . For lack of space, only the variables and constraints where action fly is involved are represented in that table, but the others are defined analogously.... ..."

### Table 2. A list of counting constraints that are intractable to propagate with GAC.

2004

"... In PAGE 5: ... We use the basic tools of computational complexity to show their tractability or intractability. Table2 gives some of the intractability results we obtained for counting constraints on integer variables. Proofs are in [3].... ..."

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