### Table 3: Comparison of monotone and non- monotone search in XRCE corpora.

"... In PAGE 5: ... In order to guar- antee a fast human interaction, in the remaining experiments of the paper, the mean iteration time is constrained to about 80 ms. Table3 shows the results using monotone search and combining monotone and non- monotone search. Using non-monotone search while the given prefix is translated improves the results significantly.... ..."

### Table 3: Comparison of monotone and non- monotone search in XRCE corpora.

"... In PAGE 5: ... In order to guar- antee a fast human interaction, in the remaining experiments of the paper, the mean iteration time is constrained to about 80 ms. Table3 shows the results using monotone search and combining monotone and non- monotone search. Using non-monotone search while the given prefix is translated improves the results significantly.... ..."

### Table 3: Algorithm for Creating an Abstraction Hierarchy Input: Operators of a problem space and, optionally, the goals of a problem. Output: An ordered monotonic abstraction hierarchy. procedure Create Hierarchy(operators[,goals]): 1.

1994

"... In PAGE 16: ... The nal hierarchy consists of an ordered set of abstraction spaces, where the highest level in the hierarchy is the most abstract and the lowest level is the most detailed. Table3 de nes the create hierarchy procedure for building ordered monotonic ab- straction hierarchies. The procedure is given the domain operators and, depending on the de nition of find constraints, may also be given the goals of the problem to be solved.... In PAGE 29: ....3.3 Abstraction Hierarchy Selection Once alpine builds the directed graph and combines the strongly connected components, the next step is to convert the partial order of abstraction spaces into a total order. The algorithm shown in Table3 uses a topological sort to produce an abstraction hierarchy. However, in general, the total order produced by the topological sort is not necessarily unique, and two abstraction hierarchies that both have the ordered monotonicity property for a given problem will di er in their e ectiveness at reducing search.... ..."

Cited by 154

### Table 12 Embedding side-effects and lazy terms

2005

"... In PAGE 25: ...A side-effect and a lazy form are combined into a sandbox expression where the root context is the combined side-effect and the value is the embedded lazy form. The functions embed and combineprime are given in Table12 . The embedding is compositional except for abstractions that respect the special nature of lazy closures.... ..."

Cited by 1

### Table 7: Criticalities for the manufacturing domain. ALPINE apos;s abstraction hierarchy violates the pre- condition monotonicity property as the Painted pre-

Cited by 5

### Table 7: Criticalities for the manufacturing domain. ALPINE apos;s abstraction hierarchy violates the pre- condition monotonicity property as the Painted pre-

1996

Cited by 5

### Table 14: Using a less constrained abstract problem solving domain: Comparison of the

1995

Cited by 3

### Table 4: Comparison with Iusem apos;s method (F monotone).

"... In PAGE 13: ... Consequently, the stopping criteria used for both algorithms in this case was: j[Fp(P (xk))]ij 10?3jdij; i = 1; : : : ; n: The results of the third set of experiments are given in Tables 3 and 4. Table 3 contains experiments where F is not necessarily monotone and Table4 contains experiments where F has been generated as in (2), so, it is monotone. In Table 3, the superscript 2 indicates that the value of the objective function (3) at the nal point was less than 10?8 and 3 indicates that the value of the objective function (3) at the nal point was 0:012.... In PAGE 13: ... In Table 3, the superscript 2 indicates that the value of the objective function (3) at the nal point was less than 10?8 and 3 indicates that the value of the objective function (3) at the nal point was 0:012. Similarly, in Table4 , 2 means that the value of the objective function (3) at the nal point was less than 10?5 and 3 means that the value of the objective function (3) at the nal point was 0:0013. For Iusem apos;s method (in Table 4) we report a triplet (number of iterations, execution time, kFp(x)k1).... In PAGE 13: ... Similarly, in Table 4, 2 means that the value of the objective function (3) at the nal point was less than 10?5 and 3 means that the value of the objective function (3) at the nal point was 0:0013. For Iusem apos;s method (in Table4 ) we report a triplet (number of iterations, execution time, kFp(x)k1). As expected, Iusem apos;s method never converged in the nonmonotone cases (at least after 50000 iterations).... In PAGE 17: ... However, the probability of such a generation tends to zero as n tends to in nity. Surprisingly, our method turned out to be also more e cient than Iusem apos;s method for most monotone problems ( Table4 ). This seems to con rm that, as ocurred in the linearly constrained minimization problem, our box-constrained approach is also practical in the VIP problem.... ..."

### Table 1: Problem 1: SRK, hydrogen sul de(1) and methane(2) at P = 40.53 bar and T = 190 K. Comparison of using natural interval extensions (F ), constrained space interval extensions (F CS), and constrained space plus monotonic interval extensions (F CSM).

1998

"... In PAGE 17: ...Newton uniqueness test described above. Thus, for example, in Table1 , for the z1 = 0.0115 feed, the x1 value found for the third root was actually x1 = [0.... In PAGE 18: ...and Gani, 1996), a code that in general we have found to be extremely reliable, incorrectly predicts that this mixture is stable. As indicated in Table1 , several other feed compositions were tested using the IN/GB approach, with correct results obtained in each case. It should be noted that the presence of multiple real volume roots in this problem does not present any di culty, since the solver simply nds enclosures of all roots for the given system.... In PAGE 18: ... Thus, nothing needs to be done to select the right volume roots (or compressibility factors). Also included in Table1 are the number of root inclusion tests performed in the computation and the total CPU time on a Sun Ultra 1/170 workstation. This is done for the case (F ) in which just the natural interval extensions are used, the case (F CS) in which the constrained space interval extension is used, and the case (F CSM) in which both the constrained space and monotonic interval extensions are used.... In PAGE 29: ... Table1 . Problem 1: SRK, hydrogen sul de(1) and methane(2) at P = 40.... ..."

Cited by 25

### Table 1: Problem 1: SRK, hydrogen sul de(1) and methane(2) at P = 40.53 bar and T = 190 K. Comparison of using natural interval extensions (F ), constrained space interval extensions (F CS), and constrained space plus monotonic interval extensions (F CSM).

"... In PAGE 9: ...c2 = 190.6 K, Pc2 = 46.0 bar, !2 = 0.008, and a binary interaction parameter k12 = 0.08. Several feed compositions were considered, as shown in Table1 , which also shows the roots (stationary points) found, and the value of the tangent plane distance D at each root. For the z1 = 0.... In PAGE 10: ... Michelsen apos;s algorithm, as implemented in LNGFLASH from the IVC-SEP package (Hytoft and Gani, 1996), a code that in general we have found to be extremely reliable, incorrectly predicts that this mixture is stable. As indicated in Table1 , several other feed compositions were tested using the interval Newton/generalized bisection approach, with correct results obtained in each case. It should be noted that the presence of multiple real volume roots in this problem does not present any di culty, since the solver simply nds all roots for the given system.... In PAGE 10: ... It should be noted that the presence of multiple real volume roots in this problem does not present any di culty, since the solver simply nds all roots for the given system. Also included in Table1 are the number of root inclusion tests performed in the computation and the total CPU time on a Sun Ultra 1/170 workstation. This is done for the case (F ) in which just the natural interval extensions are used, the case (F CS) in which the constrained space interval extension is used, and the case (F CSM) in which both the constrained space and monotonic interval extensions are used.... ..."