### Table 4. Results of theorem proving on testbed systems

1999

"... In PAGE 42: ...4 Theorem Proving Results Overall, 21 strategies were developed to assist in the analysis of ASTRAL specifications. Table4 shows the results of using PVS and the developed strategies to prove the proof obligations of the testbed systems. The results of the theorem prover proofs and earlier proofs by hand are the basis for a systematic analysis methodology described in [Kol 99b] in which tool-supported guidance is given for constructing proof sketches by hand, which are then carried out in a similar fashion within PVS.... ..."

Cited by 3

### TABLE 1 MODEL SIZE AND RELATIVE ELAPSED TIMES AS A FUNCTION

1993

Cited by 1

### TABLE A-3/M.810 Normal limits for the power per telegraph channel in FMVFT systems for other bearer circuits ulululululululululululululululululululululululululululululululululululululululululululululul

### Table 1: Performance of TGTP on theorems of the proposed system. 11

"... In PAGE 10: ...heorems can be used in proving the current theorem. Note also that theorems 25, 36..52 were proved by contradiction. All other theorems in Table1 were proved by induction. 7.... In PAGE 12: ...thm 48 41 105 3,4,10,13,15,18,19,21,R2,R5,R14,R19,R22 52 Div uniq 2.thm 49 33 293 7,9,10,11,13,16,18,19,20,21,22,R2,R3,R16,R18,R22,R23, Table1 : Performance of TGTP on theorems of the proposed system. 12S EQsxy ~+zsuy ~+zux 13S gt;EQxy ~+zux ~+zuy 14S ~EQxy ~+zux +zuy 15S gt;~+xyz +yxz 16S ~+xyz ~+zuv ~+yuw +xwv 17S gt;~+xyz +zuv ~+xwv ~+yuw 18# theorem 19S gt;+0ac 20S gt;+0bc 21S gt;~EQab Phases 1 and 2 clauses used in proof: 22: (17d,11a) ~+xyz +z0u ~+xyu 23: (22b,15a) ~+xyz ~+xyu +0zu 24: (23b,11a) ~+x0y +0yx 25: (24a,11a) +0xx 26: (20a,15a) +b0c 27: (26a,13c) EQxc ~+b0x 28: (27b,11a) EQbc 29: (21a,8b) ~EQba 30: (29a,9c) ~EQbx ~EQxa 31: (30b,13a) ~EQbx ~+yzx ~+yza 32: (31b,19a) ~EQbc ~+0aa 33: (32a,28a) ~+0aa 34: (33a,25a) [] PHASE 0: 0 s, PHASE 1: 0 s, PHASE 2: 0 s, Total Time: 0 s To begin, the top line is the name of the theorem.... ..."

### Table 1. CNF translation for a normalized Boolean circuit

### Table 1: How Theorem Provers Store Theorems This paper proposes a method by which a theorem prover can use digital signatures to detect any modi cations made to a theorem while outside the system. Using this method it is no longer necessary to store theorems toget- her with their proofs in order to ensure the security of the theorem prover. Furthermore it is perfectly safe to store theorems in a documented format. These two features make the method an ideal basis for exchanging results between di erent proof tools.

1996

"... In PAGE 3: ... Furthermore, this technique can not be used to share results with other systems, since proofs can usually be checked only by the system in which they were developed. Table1 pre- sents a summary of the methods by which various theorem provers store and reuse results.... ..."

### Table 5. Noise-temperature change versus hole diameter when the aperture plate was mounted 38.1 cm (15 in.) above the Cassegrain cone flange plane.a;b

"... In PAGE 8: ...late was raised 1.22 m (4 ft), some difierences ( gt;0.2 K) of system temperatures were observed from those shown in Table 3 for the same hole diameters. However, Table5 shows that, when the aperture plate was raised only 38.... ..."

### Table 2: Normalized power dissipation within the circuit block containing the latches

"... In PAGE 4: ...in Table2 , the total power dissipation of the circuit block is reduced by 82% by downsizing a total of 69 latches. The remaining data paths within the FUB are unchanged.... ..."

### Table 8: Comparison of upper bound on a27 a28a25a30a25a31 (predicted by Theorem 1) with the actual value of a27 a28a10a30a25a31 .

"... In PAGE 14: ... Finally, we compare the upper bound on a27 a28a25a30a10a31 provided by Theorem 1 provided with the actual value of a27a35a28a25a30a10a31 for the ISCAS 89 circuits. Table8 shows that in most cases, Theorem 1 can be used a reasonable predictor of average power consumption for a precomputed test set. 5 Conclusions We have addressed the problems of test data volume and power consumption for scan vectors for system- on-a-chip testing.... ..."