### Table 6: Comparison of best results obtained with TSSPLC and Constraint Logic Program- ming approaches. The results are in the form (TSSPLC solution, CLP solution).

1997

"... In PAGE 21: ... This con rms the observation that the initial solution quality has an impact on the performance of tabu search. The Table6 presents the comparison of the results obtained in our implementation of TSSPLC with the best ones generated by a Constraint Logic Programming approach to SPLC [HC97]. It can be veri ed that for all instances the makespan obtained by TSSPLC is less than or equals to the makespan generated with the Constraint Logic Programming algorithm described in [HC97].... ..."

### Table 12: Resolving E ect Constraints 22 The Journal of Functional and Logic Programming 1997-5

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

### Table 3: Oz and Prolog Concurrent logic programming Oz

1998

"... In PAGE 32: ... A.3 Oz and Prolog There is a strong sense in which Oz is a successor to Prolog (see Table3 ). The Oz system can be used for many of the tasks for which Prolog and constraint logic programming are used today [16, 21, 12, 24].... ..."

Cited by 1

### Table 2: Benchmark timings, in milliseconds introduced by Ramakrishnan et al. [28], and Zobel [33] studied nite dependencies as a type of Boolean dependencies. Armstrong and Delobel [2] introduced functional dependencies for rela- tional databases and Zobel [33] studied functional dependency analysis for deductive databases. The history of positive functions in program analysis is somewhat shorter. The use of positive functions was suggested for groundness analysis by Marriott and S ndergaard [24] (under the less suggestive name `Prop apos;) and further studied by Cortesi et al. [15]. Bigot et al. [4] give a precise niteness analysis which is based on positive functions. Both positive and de nite functions have been suggested as the basis for groundness analysis of constraint logic programs, normal logic programs, logic programs with dynamic scheduling and for suspension analysis of concurrent logic languages.Apart from the mentioned work on analysis, there are only few studies of the positive5 func- 5Some authors, including Chang and Keisler [9] and Dart [17] refer to what is commonly called a `monotonic apos; function as `positive. apos; We use the more common terminology (although in [24] the elements of Pos were erroneously called `monotonic apos;).

1998

"... In PAGE 28: ... Next we show the average and maximum number variables in all the clauses in the test, and nally the average and maximum number of arguments (arity) of the predicates in the test. Table2 shows the results. All times are given as the average of 5 runs of the program.... ..."

Cited by 58

### Table 1. Experimental results on a set of 10 10 benchmark problems. In a second experiment we examined whether we can compete with other algorithms. A set of 3000 10 10 job shop scheduling problems was generated and solved with a schedule construction algorithm based on constraint logic programming (CLP) known to produce good solutions [3]. Each of the 27 available variable ordering heuristics was applied and the best schedule obtained was compared with the solution generated by our algorithm. We made two runs, one with the parameters and proven to be the best to solve the ft10 benchmark problem and a second modi ed run, additionally allowing repetitions based on random re-initializations after self-organizing has failed.

1999

"... In PAGE 5: ... We varied the makespan reduction value as well as the parameter . Table1 summarizes the results, showing the best and average makespan obtained and the known optimum for each problem. Each run took about 9 seconds on a 233MHz i686 PC, the best schedule usually emerged after half the time.... ..."

Cited by 2

### Table 2. Performance Results on the Magic Series Program. Interestingly, local search performs reasonably well on this problem as indicated in Table 2. The table gives the best, average, and worst times in seconds for 50 runs on a 2.4Ghz Pentium, as well as the standard deviation. The contributions here are twofold. On the one hand, Comet naturally ac- commodates logical and cardinality operators as differentiable objects, allowing very similar modelings for constraint programming and local search. On the other hand, implementations of logical/cardinality operators directly exploit incremen- tal algorithms for the constraints they combine, providing compositionality both at the language and implementation level. The implementations can in fact be shown optimal in terms of the input/output incremental model [14], assuming optimality of the incremental algorithms for the composed constraints.

### Table 2: Transformation Table for Functional Logic Programming.

"... In PAGE 11: ... fib(1,1). 2 PAGE can model this programming paradigm introducing a new transformation table ( Table2 ) which is used in conjunction with the tables used for the LP paradigm. Now we consider that functional arguments have the same notational signi cance as the previously seen ordinary variables.... In PAGE 11: ... Functional arguments are prioritized in the uni cation procedure (the uni cation procedure becomes matching procedure since we are dealing with interpreted functional terms), so that when we have to unify a variable argument which is in the argument list of a functional argument we prefer to unify the latter and discard the former. This can easily be seen in Table 3, where the equivalent AG is given after the use of transformation Table 1 in conjunction with the transformation Table2 . Fig.... In PAGE 12: ....4.1. Multi-pass execution (simple case) The method described so far ( Table2 is used) is operationally incomplete when the minimal elements in the partial ordering induced by the generated dependency graph are unbound (for instance some of the arguments in the argument list of a functional argument are unbound). In such cases, a delayed binding mechanism has to be used.... In PAGE 12: ... 6 we can see the dependency graph for the equivalent AG corresponding to Table 5 generated after the the use of Table 1 in conjunction with Table 4. Here, we do not have functional arguments and so we do not apply the transformation Table2 . Arrows corresponding to Table 1 are designed with solid lines, while arrows corresponding to Table 4 are designed with dashed lines.... In PAGE 15: ...he new inherited attribute). This is shown in Fig. 5 with the dashed lines. 2 It is noteworthy that the same behaviour is possible if we supply the FLP tranformation table ( Table2 ) with extra transformation actions, simulating this way the constraint solver. However, that actions are problem depented and they do not t in a declarative way of programming.... ..."