### Table 4: Some inferred functions

2006

"... In PAGE 19: ... The implementations are in Common-Lisp. In Table4 we have listed experimental results for a few sample problems. Due to the restrictions of the first synthesis step all these induced programs deal with structural problems and are composed of only the primitive functions stated in Section 4.... In PAGE 21: ...nduced RPS are ex post introduced from us; the system introduces names G1, G2, . . .. multi(x) = if(empty(x), [], cons(multlasts(head(x)), if(empty(tail(x)), [], cons(unpack(head(tail(x))), if(empty(tail(tail(x))), [], cons(switch(head(tail(tail(x)))), multi(tail(tail(tail(x)))))))))) switch(x) = if(empty(tail(x)), x, cons(head(tail(x)), cons(head(x), if(empty(tail(tail(x))), [], switch(tail(tail(x))))))) unpack(x) = cons(cons(head(x), []), if(empty(tail(x)), [], unpack(tail(x)))) multlasts(x) = if(empty(tail(x)), x, cons(head(last(x)), multlasts(tail(x)))) last(x) = if(empty(tail(tail(x))), tail(x), last(tail(x))) Table 6: Recursive Program Scheme for multi Considering the times taken by the first and second synthesis step for the problems listed in Table4 one finds (1) that they depend on the number of examples for the first step and on the number of recursive equations for the second step and (2) that the times taken from the second step increase faster than the times taken from the first step. A detailed analysis of the complexities of the two synthesis steps has still to be done.... ..."

Cited by 5

### Table 1. Equational complexity of three classes of lattices

### Table 1. Equational complexity of three classes of lattices

### Table 1. Complexity of inference, model checking and computation.

1997

"... In PAGE 12: ... For long sequences (m n) this can be useful. 4 Proof Sketches In this section, we give proof sketches for some of the results of Table1 and Table 2. Theorem 9.... ..."

Cited by 17

### Table 1. Complexity of inference, model checking and computation.

1997

"... In PAGE 12: ... For long sequences (m greatermuch n) this can be useful. 4 Proof Sketches In this section, we give proof sketches for some of the results of Table1 and Table 2. Theorem 14.... ..."

Cited by 17

### Table 6 Comparisons of the lattice post-processing methods Lossless Rescorable Size Lattice accuracy

1979

"... In PAGE 26: ...orrect hypotheses). It is not appropriate for the purpose of subsequent processing. Of course one can use confusion networks to constrain the acoustic recognizer and generate new lattices for further processing, but it is more complicated and, as we have found, there is a degradation in accuracy compared to using word graph compression and likelihood pruning. Table6 compares the four post-processing methods on whether they are lossless, whether they can be rescored, their relative size, and their relative accuracy. The up-arrows and down-arrows indicate the direction of change each method has on a particular attribute.... ..."

Cited by 2

### Table 4. Inference Rules

2003

"... In PAGE 9: ...3.3 Inference Rules Table4 collects the other inference rules. It is clear that most predicates are preserved by additional actions.... In PAGE 11: ... The properties just described can be expressed as modal formulas in our logic where the assumptions appear as pre- conditions and the security properties as post-conditions to the protocol role. If the post-condition of a protocol role matches the pre-condition of another, then using the infer- ence rule C in Table4 , we can obtain properties of a bigger protocol by composing the two. In the example that we consider here, the post-condition of DH0 matches the pre- condition of CR ( DH0 furnishes the fresh data that CR requires).... ..."

Cited by 26

### Table 1: Are 2-CNF knowledge bases compilable under CIRC? We remark that \non-compilable quot; also means that CIRC allows one to represent in a compact way an exponential number of new consequences. Unsound and fast inference with NMR As mentioned in the Introduction, it has been fre- quently argued that one of the expected features of NMR was that it could account for a form of unsound, but fast, inference. The results on the computational complexity of NMR seem to contradict the possibil- ity of NMR of being faster than classical reasoning. In this section we show that NMR is more e cient in

1994

"... In PAGE 4: ... Hence the positive aspect of Theorems 2 and 4 is that circumscription is an extremely powerful tool for representing problems in a compact way. We summarize the results in Table1 , where we divide cases between the two services, and between \short quot; and \long quot; queries. By \short quot; we mean clauses of xed length (e.... In PAGE 6: ... Our results complement theirs, as we consider any possible prepro- cessing (even a non-recursive one) with the only restric- tion that the new representation can answer queries in time polynomial in the size of the original knowl- edge base. For each entry of Table1 marked \non- compilable quot;, we proved that not only no e cient basis exists but also that no other compilation is possible. Acknowledgements This work has been supported by the ESPRIT Ba- sic Research Action N.... ..."

Cited by 41

### Table 1. Observations and inferences

2001

"... In PAGE 16: ... s2 := reach forward from s1 amp; sit2 endreach; Region s2 in its turn can be intersected with the region describing the next situation the user may encounter when she switches the aileron back to blue and observes that both the fluids stopped decreasing. Note that this step corresponds to going from step 2 to step 4 in the diagnosis steps reported in Table1 , skipping the third step listed there. The resulting regions printed by HyTech of for example s1 amp; sit2 and s2 amp; sit3 gives us an indication of the size and complexity of the resulting regions.... ..."

Cited by 5