### Table 1. Comparing the performance of four symbolic partial order reduction techniques

"... In PAGE 13: ... We also set the number of threads to 2, 3, 4 for both dining philosopher and indexer examples and compared the four methods. The detailed results are given in Table1 . In Table 1, Columns 1-3 show the name of the examples, the number of BMC unrolling steps, and whether the property is true or not.... In PAGE 13: ... The detailed results are given in Table 1. In Table1 , Columns 1-3 show the name of the examples, the number of BMC unrolling steps, and whether the property is true or not. Columns 4-7 report the runtime of the four methods.... ..."

### Table 1. Experimental results for partial order reduction

1999

"... In PAGE 7: ...rties, e.g. checking separately for 3p and for 3q, rather than 3p^3q. In Table1 we present some experimental results of using partial order reduction. The experiments where performed on a SGI Challenge machine with 12 proces- sors and 1.... ..."

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### Table 1. Performance of partial order reduction algorithm

"... In PAGE 4: ...he independence checks of section 3.1. 4 Experiments and Results Our algorithms have been implemented in the POeM tool[2], which extends Murphi. We have run POeM on examples of varying sizes, and the results are shown in Table1 . Significant reduction is achieved in a number of the examples, the most dramatic of these being the dining philosophers problem, labeled DP in the table, where, for 10 philosophers, there is over 99% reduction.... ..."

### Table 4. GA performance with and without partial-order reduction

2002

"... In PAGE 12: ...Let PHILPO and AUTHPO 2 denote the reduced state spaces of PHILand AUTH2, respectively, that are explored when partial-order reduc- tion is used. Results of experiments are tabulated in Table4 .When exploring PHILPO, GA detects a deadlock only 5 times out of 50 runs.... ..."

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### Table 1. Net sizes (structurally reduced) and state spaces (full, reduced us- ing symmetry reduction, reduced using partial order reduction, and reduced combining partial order reduction and symmetry reduction).

2007

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### Table 6. Trail Improvement with Partial Order Reduction.

"... In PAGE 19: ... Hence, the experi- ments we now present can help us to understand what would happen when comparing po(f) against po(fe). Table6 depicts the results. In giop the error trail cannot be improved, which means that there is a unique path to the established state in the reduced state space, or several with the same cost.... ..."

### Table 5. Table with reduction factor due to partial-order and heuristic search

2004

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### Table 1: Results of Generalized Partial Order Analysis (GPO)

1998

"... In PAGE 7: ... A numeric overview of the results is shown in Table 1. In Table1 the number of states of the complete reacha- bility graph, the number of states of the reachability graphs derived using (generalized) partial-order analysis, as well the peak BDD sizes encountered during symbolic reacha- bility analysis, are listed for various instances of the param- eterized examples. CPU times, measured on a HP K260 with 896 MB RAM, are also included.... ..."

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### Table 1: Theories of partial ordering relations and their underlying principles.

2004

"... In PAGE 7: ... a0a2a1a1a0a2a5a8a7a10a9 a11a14a13a15a7 Atct a11a17a16a59a11a17a19 a21 a3a2 a24a26a13 a0a2a1a1a0a4a27a30a29 Atct a11 a31a32a7a10a9 a24a61a33a38a35a38a36a38a36a37a36a15a35a39a24a41a40a14a13a15a7a39a7a10a42 a33a39a43a41a44a45a43a41a40 a24a41a44a61a46a22a21a4a2a41a11 a13a72a16 a7a47a50 a13a15a7a47a50a28a46 a21 a4a2 a11a20a31 a52 a33a39a43a41a44a45a43a41a40 a50a28a54a55a24 a44 a13a39a13 Conclusions The theories of the component-of, mass-part-of, and contained-in relations presented in this paper share the fact that they all are partial orderings and satisfy the principle of extensionality. (In Table1 this is indicated by the + symbols.) That the principle of extensionality is satisfied means that at a given moment in time we can identify and distinguish masses in terms of their proper parts, complexes in terms of their components, and containers in terms of the entities they contain.... ..."

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### Table 3 depicts the results on detecting a safety error with IDA* with and without applying partial order reduction. The table shows the total number of transitions performed, the maximal peak of stored states and the length of the provided counterexamples. As in the previous set of experiments, solution quality is only lost when applying partial order reduction in the leader election algorithm. On the other hand, this is also the protocol for which the best reduction is obtained. We assume that the reason is the same as indicated in the previous set of experiments. Model Reduction States Transitions Length

2002

"... In PAGE 15: ... Table3 : Finding a safety violation with IDA* with and without reduction. 4.... ..."

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