### Table 1: Minimum time optimal control for double integrator with state and input con- straints: lower bounds on exact minimal time 3.5 achieved by solving moment problems with test functions of increasing degrees.

2007

### Table 1: Axioms for Qualitative Interval Boundary Con- straints

1997

"... In PAGE 4: ... Finally, reasoning on interval boundary constraints is as easy as reasoning with Allen apos;s relations. The axioms given in Table1 state how an interval boundary is related to it- self (reflexivity), which constraints are contradictory (con- tradiction), which constraints are weaker than others (sub- sumption), and how constraints can be composed (composi- tion). For more elaborate complete reasoning with interval boundaries, cf.... In PAGE 5: ... 3Whenever we use a temporal expression, it is also valid for corresponding spatial and degree expressions and the reasoning on the expressions involved. Most of the axioms from Table1 can easily be adapted to the definition of the extended distance structure (cf. Ta- ble 2).... In PAGE 8: ... The composition axioms (cf. Table1 for qualitative constraints and the following section for distance con- straints) are applied to pairs of constraint arrays until no more inferences can be drawn (e.g.... ..."

Cited by 3

### Table 1 Optimization Formulations: Objective and Con- straints

"... In PAGE 4: ...e. No 2, 3 and 4, are considered by taking the different forms of objective and constraint feasibility (see Table1 ). All formulations have the same design variables and bounds as the determinis- tic model (formulation 1).... In PAGE 7: ... When studying the optimization performance of var- ious formulations, it is noted that the feasible rates (be- fore confirmation) for Formulations 1 and 3 are higher than those for Formulations 2 and 4, and the evaluation time is shorter. The difficulties in solving Formulations 2 and 4 are due to the use of probabilistic feasibility constraint ( Table1 ). As shown in Fig.... ..."

### Table 4. Tilings under Execution Time Con- straint

2005

Cited by 1

### Table 17: Comparing fully connected nets without and with symmetry con- straints.

"... In PAGE 66: ...3.3, in the fully connected net (Test 17 and Table17 ), the lo- cally connected net (Test 18 and Table 18) and the wavelet nets (Test 19... ..."

### Table 2: Best relaxation results using binary con- straints.

### Table 1: Channel capacities for a selection of (d, k) con- straints.

### Table 1: The Complexity of Brave Reasoning in various Extensions of Datalog with Con- straints (Propositional Case under Stable Model Semantics)

"... In PAGE 23: ...Table 1: The Complexity of Brave Reasoning in various Extensions of Datalog with Con- straints (Propositional Case under Stable Model Semantics) Table1 sumarizes the complexity results of the previous section, complemented with other results (on the complexity of programs without constraints) already known in the literature. Therein, each column refers to a speci c form of constraints, namely: fg = no constraints, s = strong constraints, w lt; = weak constraints with priorities, w = weak constraints without priorities (i.... In PAGE 23: ...riorities (i.e., W has only one component). The lines of Table1 specify the allowance of disjunction and negation; in particular, :s stands for strati ed negation [45] and _h stands for HCF disjunction [3] (see AppendixB). Each entry of the table provides the complexity class of the corresponding fragment of the language.... In PAGE 24: ...i.e., relevance can be reduced to brave reasoning on DATALOG_;:;c). 8 Considering that DATALOG_;:;c is a linguistic extension of DATALOG_;: by constraints, it turns out that constraints do add expressive power to DATALOG_;:. However, it is not the case of strong constraints, as it can be seen from Table1 . Indeed, if we look at the various fragments of the language that di er only for the presence of strong constraints, we can note that complexity is constant (compare column 1 to 2, or 3 to 4, or 5 to 6).... In PAGE 26: ... Comparing the above DATALOG_;: program with the DATALOG_;:;c version of Example 9,10 it is quite apparent the advantage that weak constraints provide in terms of simplicity and naturalness of programming. Concluding, we would like to bring reader apos;s attention to the fragment of DATALOG_;:;c with HCF disjunction and strati ed negation ((5,6) in Table1 ): it has a very clear and easy- to-understand semantics and, at the same time, allows us to express several hard problems (up to P 2 -complete problems) in a natural and compact fashion. (In our opinion, recursion through disjunction or negation makes programs more di cult to understand).... ..."