## Stronger reduction criteria for Local First Search

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### BibTeX

@MISC{Kurbán_strongerreduction,

author = {Marcos E. Kurbán and Peter Niebert and Hongyang Qu and Walter Vogler},

title = {Stronger reduction criteria for Local First Search},

year = {}

}

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### Abstract

Abstract. Local First Search (LFS) is a partial order technique for reducing the number of states to be explored when trying to decide reachability of a local (component) property in a parallel system; it is based on an analysis of the structure of the partial orders of executions in such systems. Intuitively, LFS is based on a criterion that allows to guide the search for such local properties by limiting the “concurrent progress ” of components. In this paper, we elaborate the analysis of the partial orders in question and obtain related but significantly stronger criteria for reductions, show their relation to the previously established criterion, and discuss the algorithmics of the proposed improvement. Our contribution is both fundamental in providing better insights into LFS and practical in providing an improvement of high potential.

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(Show Context)
Citation Context ...a partial order is a problem that is known to be equivalent to that of finding a maximal matching in a bipartite graph [14]. The matching problem can then be solved with Hopcroft and Karp’s algorithm =-=[2]-=- in O(n 5 2 ), where n is the size of the bipartite graph. This is in turn, twice the size of the peak. – At last, the resulting widths have to be ordered and the test for an ndecreasing sequence has ... |

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(Show Context)
Citation Context ... the proposed improvement. Our contribution is both fundamental in providing better insights into LFS and practical in providing an improvement of high potential. 1 Introduction Partial order methods =-=[15, 5, 8, 7, 12, 16, 9, 10, 13, 4, 6]-=- exploit the structural property of independence that occurs naturally in asynchronous parallel systems. The basic observation exploited by partial order methods is the commutation of pairs of indepen... |

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(Show Context)
Citation Context ... the proposed improvement. Our contribution is both fundamental in providing better insights into LFS and practical in providing an improvement of high potential. 1 Introduction Partial order methods =-=[15, 5, 8, 7, 12, 16, 9, 10, 13, 4, 6]-=- exploit the structural property of independence that occurs naturally in asynchronous parallel systems. The basic observation exploited by partial order methods is the commutation of pairs of indepen... |

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(Show Context)
Citation Context ...th 5 states, which each choose nondeterministically, which fork they pick up first (Figure 1 at left). This is an example, where typical partial order techniques like stubborn sets [16] or ample sets =-=[12]-=- fail to achieve significant reduction; in 11spick right pick left pick right pick left drop right drop left Fig. 1. An instance of the philosophers / the “comb” process as Petri net fact, experimenta... |

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Citation Context ... the proposed improvement. Our contribution is both fundamental in providing better insights into LFS and practical in providing an improvement of high potential. 1 Introduction Partial order methods =-=[15, 5, 8, 7, 12, 16, 9, 10, 13, 4, 6]-=- exploit the structural property of independence that occurs naturally in asynchronous parallel systems. The basic observation exploited by partial order methods is the commutation of pairs of indepen... |

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Citation Context ... This commutation of independent transitions gives rise to a notion of equivalent executions, and the equivalence classes are called Mazurkiewicz traces. Among these methods, Local First Search (LFS) =-=[11, 1]-=- is specialized for the complete search for local properties, i.e. properties that can only be modified by dependent transitions. The definition and justification of LFS highly depend on the character... |

3 |
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- 2001
(Show Context)
Citation Context ... This commutation of independent transitions gives rise to a notion of equivalent executions, and the equivalence classes are called Mazurkiewicz traces. Among these methods, Local First Search (LFS) =-=[11, 1]-=- is specialized for the complete search for local properties, i.e. properties that can only be modified by dependent transitions. The definition and justification of LFS highly depend on the character... |

2 |
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(Show Context)
Citation Context ...partial order of each peak, its width has to be computed. Computing the width of a partial order is a problem that is known to be equivalent to that of finding a maximal matching in a bipartite graph =-=[14]-=-. The matching problem can then be solved with Hopcroft and Karp’s algorithm [2] in O(n 5 2 ), where n is the size of the bipartite graph. This is in turn, twice the size of the peak. – At last, the r... |