### Table 1: Syntax of SFD constraints.

"... In PAGE 5: ... 5.2 The core language: SFD The kernel of the solver is based on an unique constraint of the form X in r where X is a FD variable and r a syntactic domain de ned by Table1 . The range (syntactic domain) can be constant or can depend on some indexicals: def(X), which is the valued domain of variable X, sigma(X), which is the semiring sum of the semiring values appearing in the valued domain of variable X, min(X), which is minimal index (associated to a non-null semiring value) in the valued of variable X, max(X), which is maximal index (associated to a non-null semiring value) in the valued of variable X, val(X), which is the delayed value of variable X.... ..."

### Table 12: Strengths of Domain Constraints.

1994

"... In PAGE 21: ... It seems that in these two domains, the domain constraints are not strong enough to reduce the branching factors below that of One-Unsat. To see this conclusion more precisely, we computed the critical bound on S and S itself for each test problem (see Table12 ). As can be observed, the actual value of S is much higher than required by the... ..."

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### Table 12: Strengths of Domain Constraints.

1994

"... In PAGE 21: ... It seems that in these two domains, the domain constraints are not strong enough to reduce the branching factors below that of One-Unsat. To see this conclusion more precisely,we computed the critical bound on S and S itself for each test problem (see Table12 ). As can be observed, the actual value of S is much higher than required bythe... ..."

Cited by 6

### TABLE 6. Domain analysis for finite element computational models

### Table 4: An example of constraint solving on the domain Colour Ch.P. C

"... In PAGE 22: ...Triples Simple Interval constraints Constraints with indexicals (c1) (::0; fAg; fd1 Ag) (d1 A) A 2 [white; black] (dB A) A 2 [white; max(B)) (c2) (::0; fBg; fd1 Bg) (d1 B) B 2 [white; black] (dA B) B 2 (min(A); black] (c3) (::0; fCg; fd1 Cg) (d1 C) C 2 [white; black] (dC B) B 2 [white; max(C)) (c4) (6 =0; fA; Bg; fdB A; dA Bg) (d2 A) A 2 [white; black) (dB C) C 2 (min(B); black] (c40) (6 =0; fA; Bg; fd0B A ; d0A B g) (d2 B) B 2 (white; black] (d0B A ) A 2 (min(B); black] (c5) (6 =0; fB; Cg; fdC B; dB Cg) (d2 C) C 2 (white; black] (d0A B ) B 2 [white; max(A)) (c50) (6 =0; fB; Cg; fd0C B ; d0B C g) (d3 A) A 2 (white; black] (d0C B ) B 2 (min(C); black] (c6) (2; fAg; fd2 Ag) (d3 B) B 2 [white; black) (d0B C ) C 2 [white; max(B)) (c7) (2; fBg; fd2 Bg) (d3 C) C 2 [white; black) (c8) (2; fBg; fd3 Bg) (c9) (2; fCg; fd2 Cg) (c10) (2; fCg; fd3 Cg) (c11) (2; fAg; fd3 Ag) interval constraints used by Table4 to show the constraint solving process. Three choice points are added by the inference machine and backtracking is executed when an inconsistency or a solution is found by the generic solver.... ..."

### Table 8.1 Experimental results: comparing Quad and Constraint solvers.

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### Table 8.1 Experimental results: comparing Quad and Constraint solvers

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### Table 8.1 Experimental results: comparing Quad and Constraint solvers

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### Table 1. Experimental results: comparing Quad and Constraint solvers

"... In PAGE 11: ...entium IV processor at 2.66Ghz. The number of solutions is followed by the number of safe solutions between brackets. Table1 displays the performances of RealPaver, BP(Box+Quad(Qmid)) and BP(Box). The benchmarks have been grouped into three sets.... ..."

### Table 1. Experimental results: comparing Quad and Constraint solvers

"... In PAGE 11: ...entium IV processor at 2.66Ghz. The number of solutions is followed by the number of safe solutions between brackets. Table1 displays the performances of RealPaver, BP(Box+Quad(Qmid)) and BP(Box). The benchmarks have been grouped into three sets.... ..."