### Table 1: Lower bounds for depth 3 arithmetic circuits

"... In PAGE 3: ... In particular, this result strengthens our previous bound in the functional framework (the reason for including the latter in the paper lies in its simplicity and applicability to symmetric functions). Table1 summarizes our current knowledge about the best known lower... ..."

### Table 2: Simulated lower bounds on expected circuit depth. These bounds have not been proven but are suggested by the results of Markov chain simula- tions.

1999

Cited by 1

### Table 2: Simulated lower \bounds quot; on expected circuit depth. These \bounds quot; have not been proven but are suggested by the results of Markov chain simula- tions.

1999

Cited by 1

### Table 1: Lower bound sifting

1999

"... In PAGE 3: ... In a rst series of experiments, we compare the original sifting algorithm [14] with the lower bound improvement. Results are given in Table1 . In column circuit the name of the benchmark circuit is given and column in refers to the number of inputs of the circuit.... ..."

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### Table 1: Lower bounds on expected circuit depth. Bi is the maximum number of gates allowed on depth lr?i in the modi ed random circuit process.

1999

Cited by 1

### TABLE 10.3.1 Circuit lower bounds for range searching.

2004

Cited by 1

### TABLE 3 COMPARISON OF LOWER AND UPPER BOUNDS ON AREA WITH ACTUAL AREA REQUIREMENTS (ISCAS-85 and ISCAS-89 CIRCUITS) CIRCUIT INPUTS AREA LOWER UPPER Name # #GATES BOUND BOUND

1996

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### Table 2: Relaxed lower bound sifting nodes deviation/circuit time deviation/circuit

1999

"... In PAGE 4: ...Figure 3: CPU time in seconds (left) and size in 1000 nodes (right) for relaxing bound lb-sifting are given in Table2 . Columns 2-6 and 7-11 give informations about the behavior of the algorithms for result- ing BDD size and runtime, respectively.... ..."

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### Table 3: Lower bound

"... In PAGE 9: ...7, an optimal drawing of a K9 has 36 crossings. Referring to Table3 , an optimal drawing has at least 27 non-internal edge crossings (Lemmas 4.... ..."

### Table 3: Upper bounds, exponential distribution.

"... In PAGE 9: ... Since the rational numbers involved soon have very large nu- merators and denominators, they where rounded to double precision reals, but always upward, to assure us that we really get an upper bound. The results are summarized in Table3 .... ..."

Cited by 1