### Table 2 Transitions of weighted automata

### Table 2 Transitions of weighted automata

in Abstract QAPL 2005 Preliminary Version Metrics for Action-labelled Quantitative Transition Systems 1

### Table 4. Shared Backup Path Protection Problem Performance Parameters

"... In PAGE 14: ...# Variables Test ID # Paths SBPP PR 32LM 135 302 1,405 45LM 178 401 2,046 32HM 286 604 2,976 45HM 368 781 4,076 32LS 122 276 950 45LS 169 383 1,840 32HS 239 510 1,699 45HS 319 364 683 2,921 Table 3. Problem Characteristics for SBPP and PR Table4 illustrates that the majority of SBPP problems were not solved to optimality by either GDS or CPLEX within the 12 hour algorithm testing time limit. The star topologies appeared easier to solve.... ..."

### Table 2: Technology Mapping results

"... In PAGE 8: ... The results show that the Boolean approach reduces the number of matching algorithm calls, nd smaller area circuits in better CPU time, and reduces the initial network graph because generic 2-input base function are used. Table2 presents a comparison between SIS and Land for the library 44-2.genlib, which is distributed with the SIS package.... ..."

### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### Table 2: Some values used in and resulting from the simulations and optimizations. Note that the ight and optimization times refer to the times for the full ight paths. The machine used is a 2.8 GHz Pentium 4 PC. For each bird, the same metric weight values are used for all paths.

### 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 6: Optimization for Cellular Automata Model

2005

"... In PAGE 30: ...As indicated in Table6 , there is fairly good agreement between the recommended number of booths for a typical day and for peak hours. However, we note that the optimal booth number for a typical day never exceeds that for rush hour.... In PAGE 30: ... Rush hour seems to require slightly more booths than a typical day in order for the plaza to operate most efficiently. Each value in Table6 is representative of approximately 20 trials. Through these trials, we noted a remarkable stability in our model.... ..."