### Table 4: Bus contention checking using global v.s. local BDDs Global BDDs Local BDDs

"... In PAGE 13: ... We then study the effectiveness of the local BDD technique (with the short-circuit optimiza- tion turned on). The results ( Table4 ) show that the local BDD technique can significantly improve the perfomance of some testcases by reducing the number of aborted properties and the run time, particularly for circuits 4 and 6. The memory usage, on the other hand, remains about Table 2: Bus contention checking using PODEM v.... ..."

### Table 2. Test results for protocol mux-sem-try

"... In PAGE 10: ... In this case, when performing the computation all three phases had to be employed, together with several refinements in which multiple new variables where added and the predecessors of violating states had to be analyzed. Table2 compares forward and backward reachability to completion for mux- sem-try. Both the number of bdds and the run times achieved by completion are significantly better.... ..."

### Table 2. Test results for protocol mux-sem-try

"... In PAGE 10: ... In this case, when performing the computation all three phases had to be employed, together with several refinements in which multiple new variables where added and the predecessors of violating states had to be analyzed. Table2 compares forward and backward reachability to completion for mux- sem-try. Both the number of bdds and the run times achieved by completion are significantly better.... ..."

### Table 1. Statistics of the circuits, number of iterations and variables in the BDDs, and results obtained.

2003

"... In PAGE 5: ...he script script.algebraic. All tests were performed on a 300MHz Pentium running Linux with a CPU time limit of BG hours and memory usage restricted to BLBC MB. Table1 summarizes the obtained results. Columns 2 to 5 in this table list the statistics of the circuits, namely the number of primary inputs, primary outputs, registers and size, in literals.... ..."

Cited by 2

### Table 1. Statistics of the circuits, number of iterations and variables in the BDDs, and results obtained.

"... In PAGE 5: ...he script script.algebraic. All tests were performed on a 300MHz Pentium running Linux with a CPU time limit of a126 hours and memory usage restricted to a204 a1 MB. Table1 summarizes the obtained results. Columns 2 to 5 in this table list the statistics of the circuits, namely the number of primary inputs, primary outputs, registers and size, in literals.... ..."

### Table 3. Distributed reachability on the benchmark suite. Four examples reached flxpoint and veriflcation completed. Three examples required more workers than were available to us and therefore worker over ow occurred. The Max workers column indicates the maximum number of active workers during the computation. The run time when the veriflcation is completed is given in hours. Run time is time elapsed since the flrst worker starts to run until the last worker flnishes the run. Two measures are given for the iteration at which the sequential algorithm over ows: The sum of the sizes of the BDDs representing the subsets of reachable states, and the number of active workers at this iteration

"... In PAGE 13: ...able 2. Benchmark suite characteristics. In each example we give the step in which the memory requirements by the sequential model checker over ow and the size of the BDD representing the set of reachable states R at that step. The distributed reachability analysis results are given in Table3 . Four exam- ples reached flxpoint and the veriflcation completed.... In PAGE 14: ...checker. We next compare the results in Table3 to the results of the high performance industrial SAT model checker tool of Intel. The SAT model checker could not complete the veriflcation of any of the examples.... ..."

### Table 3: Distributed reachability on the benchmark suite. Four examples reached fixpoint and verification completed. Three examples required more workers than was available to us, therefore worker overflow occurred. The Max workers column describes the maximum number of active workers during the computation. The run time in case the verification is completed is given in hours. Two measures are given for the iteration the sequential algorithm overflows: The sum of sizes of the BDDs representing the subsets of reachable states, and the number of active workers at this iteration

"... In PAGE 11: ... The characteristics of the six test cases are given in Table 2. The distributed reachability analysis results are given in Table3 . Four examples reached fixpoint and the verification completed.... In PAGE 11: ... Three examples required more workers than was available to us at this point (we did not always have all 100 machines at our disposal), therefore worker overflow occurred at some step, always much further than the step reached by the sequential model checker. We next compare the results in Table3 to the results of the high performance industrial SAT model checker tool of Intel. The SAT model checker could not complete the verification of any of the examples.... In PAGE 11: ...hecker tool of Intel. The SAT model checker could not complete the verification of any of the examples. Computing bounded model checking with timeout of 10,000 seconds SAT reached the bounds of 85 and 94 on I3s and I3, respectively. We also compare the results in Table3 to the results obtained in previous distributed symbolic model checking [7] and [8]. In [8] a high performance model checker was used, still, s1423 reached only step 17, while the distributed algorithm reached step 19.... ..."

### Table 2. Heuristics to limit the size of the hybrid structure Limit for the size

"... In PAGE 13: ... Therefore the overhead of the heuristics to limit the size can directly be measured in comparison to BDDs. Results are reported in Table2 . Given are the number of solutions for increasing values of n and run times in CPU seconds for BDDs and the two heuristics introduced in Section 4.... ..."

### Table 3: Symmetry Detection Times.

1994

"... In PAGE 14: ... The larger di erences are due to di erent numbers of iterations to reach convergence. Table3 gives the times required to run the symmetry check once the BDDs are built. For our method, this corresponds to the time required by the one pass of sifting done after the BDDs are built for all primary outputs.... ..."

Cited by 52

### Table 2: BDDs on Multiple Workstations.

1996

Cited by 20