### Table 3: Left: Average size of a data slice, Right: Average time in seconds to compute a data slice.

2001

"... In PAGE 13: ... Data for povray3 are not in the table for the same reason. Table3 shows these two measurements when the pointer information is provided by MoPPA (Mo) or FICS (FI). The table also shows the reduction in the size of a data slice (Reduc) when the pointer information is provided by MoPPA.... ..."

Cited by 17

### Table 3: Left: Average size of a data slice, Right: Average time in seconds to compute a data slice.

2001

"... In PAGE 13: ... Data for povray3 are not in the table for the same reason. Table3 shows these two measurements when the pointer information is provided by MoPPA (Mo) or FICS (FI). The table also shows the reduction in the size of a data slice (Reduc) when the pointer information is provided by MoPPA.... ..."

Cited by 12

### Table 1: Timed automata for L

1996

"... In PAGE 8: ...3 (Associated timed automaton) Let p 2 L. ncv, the predicate of non-con ict of variables is de ned inductively according to rules in Table1 . For all process p such that ncv(p) the timed automaton associated to p is de ned by [[p]]T = (L; A; C; p; - ; @; ) where -, @ and are de ned as the least sets satisfying the rules of Table 1.... In PAGE 10: ... But it can be straightforwardly proven by induction on the depth of the proof tree taking into account that if ; 0 2 (C) then ^ 0; _ 0 2 (C). 2 Rules in Table1 capture the behaviour described in Section 3.1 in terms of timed automata.... In PAGE 10: ... For instance, consider the term p (x 2) (fjxjg (x = 1)7!a; stop). Clearly, x is free in the invariant (x 2), however, using rules in Table1 , we derive @(p) = (x 2) and (p) = fxg. Thus, according to De nition 2.... In PAGE 11: ... De nition 3.6 (Associated timed automaton) Let E be a recursive speci cation such that ncv(E) holds according to rules in Table1 and Table 2, i.... In PAGE 11: ...able 1 and Table 2, i.e., E does not have con ict of variables. The timed automaton associated to p 2 Lv is de ned by [[p]]T = (L; A; C; p; -; @; ) where -, @ and are de ned as the least set satisfying rules in Table1 and rules in Table 2. 2 Table 2: Timed automata for recursion The following rules are de ned for all X = p 2 E ncv(X) ncv(p) ncv(X = p) 8X = p 2 E: ncv(X = p) ncv(E) (p[p=X]) = C (X) = C @(p[p=X]) = @(X) = p[p=X] a; - p0 X a; - p0 De nition 3.... ..."

Cited by 48

### Table 1. Timed automata for L

"... In PAGE 6: ... But it can be straightforwardly proven by induction on the depth of the proof tree taking into account that if ; 0 2 (C) then ^ 0; _ 0 2 (C). Rules in Table1 capture the behaviour above described in terms of timed automata. In particular, it deserves to notice that a process p + q can idle as long as one of them can.... In PAGE 6: ... For instance, consider the term p (x 2) (fjxjg (x = 1)7!a; stop). Clearly, x is free in the invariant (x 2), however, using rules in Table1... In PAGE 8: ...-; @; ) where -, @ and are de ned as the least set satisfying rules in Table1 and rules in Table 2. u t Table 2.... ..."

### Table 1: Timings for loading data slices into texture memory (in seconds)

"... In PAGE 6: ... Our volume and pixel interleaving scheme keeps processors with the same amount of data and reduces the number of pixels read back from the frame buffer. Table1 and 2 shows timings for all datasets and all screen sizes tested. Both stages scale well with the number of processors.... ..."

### Table 1: Timings for loading data slices into texture memory (in seconds)

"... In PAGE 6: ... Our volume and pixel interleaving scheme keeps processors with the same amount of data and reduces the number of pixels read back from the frame buffer. Table1 and 2 shows timings for all datasets and all screen sizes tested. Both stages scale well with the number of processors.... ..."

### Table 2: Best data bucket recovery times (seconds) and slice sizes.

"... In PAGE 37: ....g., 10 times smaller. The experiments with our earlier architectures are in [M03]. They show the clear superiority of our current implementation. Table2 completes Figure 8 by listing the T, P, C times for s values minimizing T and k = 1,2,3. We used GF(28) and GF(216).... In PAGE 38: ... As discussed in Section 3.4, we used the logarithms of the coefficients in H-1 to obtain the recovery times in Table2 . We also experimented using H-1 directly.... ..."

### Table 2-3 Primitive channels and their constraint automata

"... In PAGE 10: ... Table2 -1 Primitive channels .... In PAGE 10: ...able 2-1 Primitive channels .............................................................................................. 9 Table2 -2 Reo operations.... In PAGE 10: ...able 2-2 Reo operations.................................................................................................. 16 Table2 -3 Primitive channels and their constraint automata.... In PAGE 21: ...Graphical Representation sync Filter(pat) lossySync syncDrain syncSpout(pat) fifo asyncDrain asyncSpout(pat) Table2 -1 Primitive channels 2.... In PAGE 28: ...Reo provides a set of operations to be used by active entities inside a component instance. Table2 -2 shows the operations provided by Reo. Here we introduce three operations, read, take, and write that we will use in our implementations.... In PAGE 28: ... write Writes a data item to a source channel end if the channel end can accept it. Table2 -2 Reo operations. 2.... In PAGE 31: ... In a constraint automaton of any Reo circuit, the automata states represent the possible configurations and the automata transitions represent the possible data flow and the effect of them on configurations. Table2 -3 shows the constraint automata for Reo primitive channels. Constraint automata also serve as acceptors for timed data streams or TDS-languages.... ..."

### Table 3: Growing Automata with the Capability and the Size of an Electronic Computer # of ops. # of steps total time time per step size

1995

"... In PAGE 13: ... In order to t in the same space as the electronic computer, each element can take up at most 0:09 n m3. Results for problem sizes of 109, 1012, 1015, and 1018 operations are calculated in Table3 . The number of operations column shows the total number of operations n which are required to solve the problem.... In PAGE 13: ... The size column shows the cube side of one element of the growing automaton, assuming that each element occupies a cube. The numbers in Table3 provide an estimate for the performance of growing automata to equal electronic computers in execution speed. The most interesting column is time per step which gives the time available for the creation of new elements.... In PAGE 13: ... It can be concluded that, with the increasing problem size, time constraints considerably favor growing automata over electronic computers. It is interesting to compare the numbers in Table3 to cells in living organisms. Data are taken from Dyson (1978).... In PAGE 13: ... The rate of cell growth varies between twenty minutes and one day, approximately, for one cell division. The row that corresponds to these numbers in Table3 is the row with around 1015 operations. It follows that an implementation of growing automata with cells similar to cells in living organisms would be better than electronic computers at tasks that require at least 1015 operations.... ..."

Cited by 1

### Table 3: Growing Automata with the Capability and the Size of an Electronic Computer # of ops. # of steps total time time per step size

1995

"... In PAGE 13: ... In order to t in the same space as the electronic computer, each element can take up at most 0:09 n m3. Results for problem sizes of 109, 1012, 1015, and 1018 operations are calculated in Table3 . The number of operations column shows the total number of operations n which are required to solve the problem.... In PAGE 13: ... The size column shows the cube side of one element of the growing automaton, assuming that each element occupies a cube. The numbers in Table3 provide an estimate for the performance of growing automata to equal electronic computers in execution speed. The most interesting column is time per step which gives the time available for the creation of new elements.... In PAGE 13: ... It can be concluded that, with the increasing problem size, time constraints considerably favor growing automata over electronic computers. It is interesting to compare the numbers in Table3 to cells in living organisms. Data are taken from Dyson (1978).... In PAGE 13: ... The rate of cell growth varies between twenty minutes and one day, approximately, for one cell division. The row that corresponds to these numbers in Table3 is the row with around 1015 operations. It follows that an implementation of growing automata with cells similar to cells in living organisms would be better than electronic computers at tasks that require at least 1015 operations.... ..."

Cited by 1