### Table 1. mChaff performance. All times are in seconds (of total elapsed wall-clock time). For sizes larger than presented, enumeration of solutions for automatically con- structed symmetry-breaking predicates takes longer than 1 hour.

2003

"... In PAGE 9: ... 5.1 Benchmarks Table1 presents the results of mChaff for a set of benchmark formulas that represent structural invariants. Each benchmark is named after the class for which data structures are generated; the structures also contain objects from other classes.... In PAGE 9: ... 5.2 Performance of mChaff Table1 shows results for several input sizes for each benchmark. All scope pa-... ..."

Cited by 9

### Table 1: Cost of encoding the connectivity of a tetrahedron and eight meshes con- structed by recursive triangle quadrisection with the MPEG-4 3D Meshcoder. T: num- berofmeshtriangles,B:costtoencodeconnectivityinbits,B/Taveragecosttoencode connectivity, in bits per triangle.

2001

"... In PAGE 2: ... T: num- berofmeshtriangles,B:costtoencodeconnectivityinbits,B/Taveragecosttoencode connectivity, in bits per triangle. For example, Table1 shows the cost of encoding the connectiv- ity of a tetrahedron and eight meshes constructed by recursive tri- angle quadrisection with the MPEG-4 3D Mesh coder [8] in single- resolution mode [12]. Note that, the total cost of encoding a quadri- sected mesh is about twice the cost of encoding the original mesh BUB4BGCCB5 AP BEBUB4CCB5, while if optimally encoded, the incremental cost should be constant BUB4BGCCB5 BP BUB4CCB5B7C7B4BDB5, corresponding to the number of bits used to represent the instruction specifying the subdivision operation in the compressed bitstream.... ..."

Cited by 4

### Table 1: Cost of encoding the connectivity of a tetrahedron and eight meshes con- structed by recursive triangle quadrisection with the MPEG-4 3D Meshcoder. T: num- berofmeshtriangles,B:costtoencodeconnectivityinbits,B/Taveragecosttoencode connectivity, in bits per triangle.

2001

"... In PAGE 2: ... T: num- berofmeshtriangles,B:costtoencodeconnectivityinbits,B/Taveragecosttoencode connectivity, in bits per triangle. For example, Table1 shows the cost of encoding the connectiv- ity of a tetrahedron and eight meshes constructed by recursive tri- angle quadrisection with the MPEG-4 3D Mesh coder [8] in single- resolution mode [12]. Note that, the total cost of encoding a quadri- sected mesh is about twice the cost of encoding the original mesh BUB4BGCCB5 AP BEBUB4CCB5, while if optimally encoded, the incremental cost should be constant BUB4BGCCB5 BP BUB4CCB5B7C7B4BDB5, corresponding to the number of bits used to represent the instruction specifying the subdivision operation in the compressed bitstream.... ..."

Cited by 4

### Table 2. Whereas our baseline language model was con- structed after removing all punctuation marks from the origi- nal training text, the new language model had training text that included commas and had three acoustic models for each comma and sentence beginning; silence, /e/, and /eh/.

1999

Cited by 3

### Table 3: Example implementation of signcryption In section 3 we discuss a particular mode of opera- tion for ATM networks that use special cells for tra c management. We use signcryption primitive to con- struct a cryptogram that is carried in these special cells to implement security services.

1997

Cited by 3

### Table 3: The morphology can mutate in various ways. Off- spring are tested to make sure they can be properly con- structed, for example that no block occupies the same space. If their offspring is not viable, its genotype is discarded and another offspring is produced. This is repeated until a viable offspring is generated.

2004

Cited by 1

### Table 2: Subset of the substitution probability table con- structed with Equation (3). For each column, the number in the first row corresponds to the probability of playing the associated chord with no substitution. The numbers in the following rows correspond to the probability of play- ing the associated chord instead of the chord in the first row of the same column.

"... In PAGE 4: ... With possible values going from 0 to arbi- trary high values, the parameter allows the substitution probability table to go from the uniform distribution with equal entries everywhere (such that every chord has the same probability of being played) to the identity matrix (which disallow any chord substitution). Table2 shows substitution probabilities obtained from Equation (3) for chords in Table 1. 3 Graphical Model Graphical models (Lauritzen, 1996) are a useful frame- work to describe probability distributions where graphs are used as representations for a particular factorization of joint probabilities.... ..."

### Table 1: Mapping an EPC connector c 2 C onto places, transitions, and arcs.

"... In PAGE 10: ... N (EPC ) = (P PN; T PN; F PN) is the Petri net generated by EPC : P PN = E [ (Sc2C P PN c ), T PN = F [ (Sc2C T PN c ), and F PN = (A \ ((E F ) [ (F E))) [ (Sc2C F PN c ). See Table1 for the definition of P PN c , T PN c , and F PN c . The places in the Petri net correspond either to events or to constructs needed to model the behavior of a connector in the event-driven process chain.... In PAGE 13: ...In Table1 it is assumed that connectors are only connected to functions and events, i.... In PAGE 13: ....e., A\(C C) = ;. Although it is possible to extend Table1 with additional rules for connections between connectors, we use an alternative approach. Every arc connecting two connectors is replaced by an event and a function, i.... In PAGE 15: ... The only way to obtain a place with multiple output arcs is the mapping of XOR-split connectors onto Petri net con- structs (see Figure 4). However, the rules given in Table1 guarantee that the out- put transitions have identical sets of input places. Therefore, the Petri net is free- choice.... ..."

### Table 1: Mapping an EPC connector c 2 C onto places, transitions, and arcs.

"... In PAGE 10: ... N (EPC )=(P PN ;;T PN ;;F PN ) is the Petri net generated by EPC : P PN = E [ ( S c2C P PN c ), T PN = F [ ( S c2C T PN c ), and F PN =(A \ ((E F ) [ (F E))) [ ( S c2C F PN c ) . See Table1 for the definition of P PN c , T PN c , and F PN c . The places in the Petri net correspond either to events or to constructs needed to model the behavior of a connector in the event-driven process chain.... In PAGE 13: ...In Table1 it is assumed that connectors are only connected to functions and events, i.... In PAGE 13: ....e., A\(C C)=;;. Although it is possible to extend Table1 with additional rules for connections between connectors, we use an alternative approach. Every arc connecting two connectors is replaced by an event and a function, i.... In PAGE 15: ... The only way to obtain a place with multiple output arcs is the mapping of XOR-split connectors onto Petri net con- structs (see Figure 4). However, the rules given in Table1 guarantee that the out- put transitions have identical sets of input places. Therefore, the Petri net is free- choice.... ..."

### Table 1 Worst-case time and space for Bottleneck Recombination History on k sequences of total length n. For multiple-crossover recombination, the number of hyperedges in the hypergraph con- structed during preprocessing is m, the maximum length of a sequence is l, and the maximum number of crossovers allowed per recombination in multiple-crossover recombination without point mutation is c.

1998

"... In PAGE 5: ... 2 Note that this models pure recombination when the cost of point mutation exceeds cost bound d. Table1 summarizes the time and space of our algorithms for Bottleneck Recombination History. The algorithms consist of a preprocessing phase, which analyzes the sequence data, followed by a search phase, which tests candidate protopairs.... ..."

Cited by 28