### Table 3: Strong equivalence for expansion stop[r] stop

1994

"... In PAGE 6: ... Expansion corresponds to some sort of substitution driven by the mapping r, where however simple syntactic substitution is not always satisfactory (see [16] for an extensive discussion). Table3 gives a number of properties for expansion which are assumed to hold under any reasonable equivalence. It is a well-known fact that the standard (interleaving) semantics is not adequate Table 2: Laws of strong equivalence B [] stop B B1 [] B2 B2 [] B1 B1 [] (B2 [] B3) (B1 [] B2) [] B3 B1; (B2; B3) (B1; B2); B3 B1 j[A]j B2 B2 j[A]j B1 X ... In PAGE 8: ...r Buf such that Dbl1 Buf [r]. By applying the -distribution laws for expansion in Table3 it can be proved that Dbl1 equals Buf above after replacing Cell with Cell 1 := wg1; y2D1;z2D2wry; wrz; (wg2 jjj rg1; rdy; rdz; rg2) : This behaviour is depicted in Figure 3. Note that in Dbl1, data values are written and read two at a time.... ..."

Cited by 8

### Table 8 All the inference systems strong equivalences finite expressions all expressions

### Table 3: The numbers of essential edges with the strongly equivalent grammars for Section 02 of WSJ Parser

"... In PAGE 3: ... In order to estimate the degree of CF approxima- tion, we measured the number of essential (inactive) edges of phase 1. Table3 shows the number of the essential edges. The number of essential edges pro- duced by PB is much larger than that produced by TNT.... ..."

### Table 8 All the inference systems strong equivalences finite expressions all expressions

### Table 8 All the inference systems strong equivalences finite expressions all expressions

### Table 5.4: Statistics for the Manager OM-protocol entity model, compositional approach The Agent OM-protocol entity. For the Agent OM-protocol entity, the compositional ap- proach is used as well. An LTS was generated for the Upper Protocol Functions, and one LTS was generated for the Lower Protocol Functions. These LTSs were reduced modulo strong equivalence and subsequently combined into a new LTS. This LTS in turn, representing the APE, was reduced modulo strong equivalence. Statistics can be found in table 5.5. The calculation of the Lower Protocol Functions were clearly harder than the Upper Protocol Functions. For instance, the calculation of the Lower Protocol Functions for the MPE took more than 30 minutes, whereas the Upper Protocol Functions for the MPE took less than 30 seconds. Combining these two LTSs is a matter of minutes. Clearly, using the non-compositional approach 65

### Table 2 gives equivalent results for a mildly anisotropic case, with the strong coupling lying at an angle of 23 to the x-axis. h?1

"... In PAGE 7: ... Table2 : Number of iterations (cpu time) [number of restarts] for = 10?3, = 23 . For this problem the spectrum is less clustered, leading to a deterioration in performance of unpreconditioned CG.... ..."

### Table 2: Production-rule stack equivalents to solutions by monkey subjects and by two-tier models undergoing various forms of training. The distribution of solutions is strongly determined by the order training pairs are presented.

"... In PAGE 10: ...ross of these (e.g. [s(A)a(E)s(B)]). See Table2 for a complete list. Although the rules learned by the average (failing) agents without a training regime have a very different order, they still perform fairly well.... In PAGE 10: ... 4.3 Rule Learning with Phased Training Using the training regime for real children (Table 1), the full model can learn far more reliably ( Table2 , example in Figure 6). The multi-vector model is somewhat more like the squirrel monkeys than the children in that it more reliably learns TI than children given the same training regime.... In PAGE 11: ... This indicates the monkeys were also still learning. However, some two-tier agents showed performance degradation during trigram training (see after training columns in Table2 ). Fig- ure 7 shows one cause for this failure: a slow-learning agent that fails to find a stable solution has two priorities converge, which can lead to incorrect choices if these are both selects or both avoids.... ..."

### Table 1. Properties of Strong Emitters

"... In PAGE 5: ...he Lowenthal et al. object. In the HDF there are #0Cve objects in the #0Celd with observed equivalent widths in excess of 77 #17 A and with N#3C25, and in SSA22 there are seven such objects with N #14 25:5. The #0Duxes, equivalent widths, V magnitudes, and colors of the objects are summarized in Table1 . The equivalent widths of most of the objects are such that they are unlikely to be #5BO ii#5D emitters since the rest frame #5BO ii#5D equivalent width rarely exceeds 100 #17 A#28e.... In PAGE 6: ... 4 we plot the locus of the #28V ,I#29vs#28B,V#29 colors for the narrow-band selected objects in the LRIS #0Celds, and compare these to the color distribution of V -selected catalog objects in the HDF proper, and V -selected objects in the LRIS image of the SSA22 #0Celd. The objects that meet our equivalent width criterion and which are bright enough in the continuum for colors to be measured #28 Table1 #29 #28solid squares#29have predominantly red #28B,V #29 colors, but are blue #28or close to #0Dat-spectrum f #17 #29in#28V,I#29 colors, as would be expected for high-redshift objects that are dominated by star formation #28Cowie 1988; Songaila, Cowie, amp; Lilly 1990; Steidel et al.... In PAGE 7: ...6 to 26.5 #28 Table1 #29. ToaV =25:5 magnitude limit a color criterion #28B,V #29 #3E 1:1, #28V ,I#29 #3C 1:6 of the type discussed above gives 72 objects within the sample area when known low-redshift galaxies or stars are excluded.... In PAGE 8: ....7 #28Brocklehurst 1971#29. Because of the e#0Bects of extinction the Ly#0B luminosity is likely to underestimate the SFR, while if some portion of the Ly#0B luminosityispowered byAGN we will overestimate the SFR. The size of these e#0Bects is not easy to estimate, though the rest-frame equivalent widths of the lines #28 Table1 #29 imply that if the objects are photoionized that extinction cannot reduce the line luminosities by more than a factor of about two before reasonable theoretical upper bounds on the equivalent width #28Charlot amp; Fall 1993#29 are exceeded. We also note that in the spectra obtained to date of the SSA22 emitters #28Hu et al.... In PAGE 20: ... The colors of emission-line objects in these magnitude-selected catalogues with equivalent widths in excess of 77 #17 A in the observed frame are indicated with squares, and may be seen to lie at red #28B,V #29 and blue #28V ,I#29 colors. Two of the strong emission-line objects in the SSA22 #0Celd have continuua which are either undetected or too fainttoprovide color measurements #28 Table1 #29. They are indicated schematically by open squares placed at nominal color positions.... ..."

### Table 3 uses this approach to develop an interaction matrix that is symmetrical about the main diagonal. Consistent with the concept of correlation, the matrix assumes that the interaction of CTs is mutually equivalent. For example, studies in Stochastic processes will produce a strong positive impact on

"... In PAGE 4: ...rows. Table3 . Interaction Matrix for Curricular Topics Note: High interaction = 9/13=0.... ..."