### Table 1. Benchmark formulae

"... In PAGE 8: ... [18] which, following the CUDD naming scheme, will henceforth be referred to as bddOverApprox and remapOverApprox respectively. Table1 presents details of the Boolean functions, drawn from the MCNC and ISCAS benchmark circuits, used to assess the widening. For ease of reference, all Boolean functions are labelled with a numeric identifler.... In PAGE 10: ... The lower graph thus reports how the density varies with k. By comparing the densities reported in Table1 against those presented in the graph, it can be seen that the widening can signiflcantly improve on the density of the original ROBDD. 5.... In PAGE 10: ... The second and third columns give the size of the approximating ROBDD and the number of minterms in its un- derlying Boolean function. The fourth and flfth columns detail the ratio of these values with respect to the size and number of minterms in the original ROBDD (as given in Table1 ). The bddOverApprox and remapOverApprox algorithms are parameterised by a quality parameter q 2 [0; 1], that specifles the minimal acceptable density improvement.... ..."

### Table 1: Estimate of Boolean formula size, determined by number of Boolean operators ( and , or , not )

"... In PAGE 4: ... We estimate the length of the formula as the total count of these operators. For example, Table1 contains the estimates for our three test families, from scope = 1 through scope = 4. The size of the formula quickly becomes very large (and our simple utility is extremely inefficient and thus quickly runs out of memory); therefore, we did not compute our estimates past scope 4.... ..."

### Table 1: Estimate of Boolean formula size, determined by number of Boolean operators ( and , or , not )

"... In PAGE 4: ... We estimate the length of the formula as the total count of these operators. For example, Table1 contains the estimates for our three test families, from scope = 1 through scope = 4. The size of the formula quickly becomes very large (and our simple utility is extremely inefficient and thus quickly runs out of memory); therefore, we did not compute our estimates past scope 4.... ..."

### Table 1 Translation from state to Boolean formulas

2007

"... In PAGE 8: ...mations of Table1 , we give its encoding in terms of Bes in Table 2. Even if Ys,e is a disjunctive variable, it has only one successor: true or false.... ..."

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### Table 1: Boolean Formulas for Permutation Groups

### TABLE 14. Veri cation results wrt. the minimized models (continued) Minimized Formula 2 Formula 5 Formula 7 Formula 9

### Table 1: Estimate of Boolean formula size, determined by number of Boolean operators (\and quot;, \or quot;, \not quot;)

"... In PAGE 4: ... We estimate the length of the formula as the total count of these operators. For example, Table1 contains the estimates for our three test families, from scope = 1 through scope = 4. The size of the formula quickly becomes very large (and our simple utility is extremely ine cient and thus quickly runs out of memory); therefore, we did not compute our estimates past scope 4.... ..."

### Table 2. Experimental results for performance of di erent automata-based encodings of integer arithmetic constraints and boolean formulas. Time mea- surements appear in seconds.

"... In PAGE 16: ...7. In Table2 , we show the types and the number of xpoint iterations (F denotes the forward xpoint com- putation, EG and EF denote the xpoint computations for corresponding CTL operators), and the number of integer and boolean variables for each problem in- stance. For each version of the veri er we recorded the following statistics: 1) Time... ..."

### TABLE 11. Veri cation results wrt. the non-minimized models Non-minimized Formula 1 Formula 3 Formula 4 Formula 6 Formula 8

### Table 1. The hard ESPRESSO Problems. logic minimization, and is the starting point of our work on this domain.

1993

"... In PAGE 5: ... We deal with the 2-level logic minimization of a multi-output Boolean function f by using a one-to-one mapping between the implicants of f and those of a par- tially de ned single output Boolean function computed from f, as shown in [8, 7]. Table1 describes the 20 hard ESPRESSO problems [13, 16] and some other hard examples. It gives the numbers of input and of output (i/o) of each multi-output func- tion, and a \ quot; indicates that it is partially de ned.... ..."

Cited by 10