### Abstract

Original language | English |
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Publisher | arXiv.org |

Number of pages | 17 |

Publication status | Published - 27 Nov 2015 |

### Fingerprint

### Keywords

- Sparse matrix
- Wavefront
- Event locality
- Petri net
- METIS-316833
- Profile
- EWI-26751
- IR-99727
- Symbolic model checking
- Event span
- Bandwidth
- Decision diagram

### Cite this

*Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Model Checking*. arXiv.org.

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**Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Model Checking.** / Meijer, Jeroen; van de Pol, Jan Cornelis.

Research output: Working paper › Professional

TY - UNPB

T1 - Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Model Checking

AU - Meijer, Jeroen

AU - van de Pol, Jan Cornelis

N1 - eemcs-eprint-26751

PY - 2015/11/27

Y1 - 2015/11/27

N2 - We demonstrate the applicability of bandwidth and wavefront reduction algorithms to static variable ordering. In symbolic model checking event locality plays a major role in time and memory usage. For example, in Petri nets event locality can be captured by dependency matrices, where nonzero entries indicate whether a transition modifies a place. The quality of event locality has been expressed as a metric called (weighted) event span. The bandwidth of a matrix is a metric indicating the distance of nonzero elements to the diagonal. Wavefront is a metric indicating the degree of nonzeros on one end of the diagonal of the matrix. Bandwidth and wavefront are well studied metrics used in sparse matrix solvers. In this work we prove that span is limited by twice the bandwidth of a matrix. This observation makes bandwidth reduction algorithms useful for obtaining good variable orders. One major issue we address is that the reduction algorithms can only be applied on symmetric matrices, while the dependency matrices are asymmetric. We show that the Sloan algorithm executed on the total graph of the adjacency graph gives the best variable orders. Practically, we demonstrate that our work allows to call standard sparse matrix operations in Boost and ViennaCL, computing very good static variable orders in milliseconds. Future work is promising, because a whole new spectrum of more off-the-shelf algorithms, including metaheuristic ones, become available for variable ordering.

AB - We demonstrate the applicability of bandwidth and wavefront reduction algorithms to static variable ordering. In symbolic model checking event locality plays a major role in time and memory usage. For example, in Petri nets event locality can be captured by dependency matrices, where nonzero entries indicate whether a transition modifies a place. The quality of event locality has been expressed as a metric called (weighted) event span. The bandwidth of a matrix is a metric indicating the distance of nonzero elements to the diagonal. Wavefront is a metric indicating the degree of nonzeros on one end of the diagonal of the matrix. Bandwidth and wavefront are well studied metrics used in sparse matrix solvers. In this work we prove that span is limited by twice the bandwidth of a matrix. This observation makes bandwidth reduction algorithms useful for obtaining good variable orders. One major issue we address is that the reduction algorithms can only be applied on symmetric matrices, while the dependency matrices are asymmetric. We show that the Sloan algorithm executed on the total graph of the adjacency graph gives the best variable orders. Practically, we demonstrate that our work allows to call standard sparse matrix operations in Boost and ViennaCL, computing very good static variable orders in milliseconds. Future work is promising, because a whole new spectrum of more off-the-shelf algorithms, including metaheuristic ones, become available for variable ordering.

KW - Sparse matrix

KW - Wavefront

KW - Event locality

KW - Petri net

KW - METIS-316833

KW - Profile

KW - EWI-26751

KW - IR-99727

KW - Symbolic model checking

KW - Event span

KW - Bandwidth

KW - Decision diagram

M3 - Working paper

BT - Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Model Checking

PB - arXiv.org

ER -