### Table 1: Decidability and complexity of higher order matching

1999

"... In PAGE 2: ... The proof may be however in an obvious way changed to apply also to the pure language. Thus all lower bounds shown in Table1 apply to pure languages (without constants), while upper bounds hold for arbitrary signatures. In this paper we show that although the second and third order matching are both NP-complete, the third order case is somewhat harder in the following sense: the second order matching is in PTIME if the number of unknowns is bounded by a constant, while the third order case is NP-hard even with only one unknown variable.... ..."

Cited by 2

### Table 6.1 : Specifying a Dynamic Slice for Higher-Order Imperative Programs

### Tabling for higher-order logic programming

2003

Cited by 17

### Table 4: Higher-Order Economic Losses

"... In PAGE 5: ...oss at a single site is $3.6 million. In addition to environmental losses, other higher-order eco- nomic losses are possible in a large New Madrid earthquake. Table4 lists some of these higher-order losses and the pa- rameters that influence their levels (Eguchi et al., 1993; Wiggins, 1994).... ..."

### Table 7. Free higher-order monoid.

"... In PAGE 17: ...e., the monoid a233 a87a172 whose elements are generated by the inference rules in Table7 ), and each term constant a222 a209 a208 is mapped into a basic arrow a125a125 a222 a16a126a126 a209 a59 a218 a125a125 a208 a126a126 (where a125a125 a208 a126a126... ..."

### Table 4. Summary of higher-order strategies

"... In PAGE 9: ... All descriptor lists are then concatenated to build a single list before substitutions are performed. Table4 lists the strategies provided; several are discussed below. I invoke command amp;rest expr-specs This strategy is used to invoke command after applying substitutions extracted by evaluating the expression specifications expr-specs.... ..."

### Table 4. Summary of higher-order strategies

in NASA/CP-2003-212448 Design and Application of Strategies/Tactics in Higher Order Logics Edited by

2003

"... In PAGE 58: ... All descriptor lists are then concatenated to build a single list before substitutions are performed. Table4 lists the strategies provided; several are discussed below. I invoke command amp;rest expr-specs This strategy is used to invoke command after applying substitutions extracted by evaluating the expression specifications expr-specs.... In PAGE 72: ...65 mrd Table4 . Comparing Combinations of Provers on the uHOL Problem Set.... ..."

### Table 4. Summary of higher-order strategies

"... In PAGE 9: ... All descriptor lists are then concatenated to build a single list before substitutions are performed. Table4 lists the strategies provided; several are discussed below. invoke command amp;rest expr-specs This strategy is used to invoke command after applying substitutions extracted by evaluating the expression specifications expr-specs.... ..."

### Table 2. A set of examples and the corresponding set of clauses K (unit propagated), illustrating the effect of higher-order redundancy.

2005

"... In PAGE 9: ... Example 4. Consider the example in Table2 where the target network comprises the set of constraints {=12, =13, =23} and all negative examples differ from the single pos- itive example by at least two constraints. The version space in this example contains 4 possible constraints for each scope, due to the disjunction of possible reasons that would classify the negative examples correctly.... ..."

Cited by 5

### Table 4 lists some of these higher-order losses and the pa-

"... In PAGE 5: ... Table4 : Higher-Order Economic Losses I. Direct Losses to Petroleum Industry A.... ..."