## Distributed LTL Model Checking Based on Negative Cycle Detection (2001)

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Citations: | 33 - 13 self |

### BibTeX

@MISC{Brim01distributedltl,

author = {Lubos Brim and Ivana Cerna and Pavel Krcal and Radek Pelanek},

title = {Distributed LTL Model Checking Based on Negative Cycle Detection},

year = {2001}

}

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### Abstract

This paper addresses the state explosion problem in automata based LTL model checking. To deal with large space requirements we turn to use a distributed approach. All the known methods for automata based model checking are based on depth first traversal of the state space which is difficult to parallelise as the ordering in which vertices are visited plays an important role. We come up with entirely different approach which is dependent on locating cycles with negative length in a directed graph with real number length of edges. Our method allows reasonable distribution and the experimental results confirm its usefulness for distributed model checking.

### Citations

8940 |
Introduction to Algorithms
- Cormen
- 2001
(Show Context)
Citation Context ...iff G A has a negative cycle reachable from s.100 Luboˇs Brim et al. 4Distributed Negative Cycle Detection Algorithm The general sequential method for solving the SSSP problem is the scanning method =-=[11,8]-=-. For every vertex v, the method maintains its distance label d(v), parent vertex p(v) and status S(v) ∈{unreached, labelled, scanned}. The subgraph Gp of G induced by edges (p(v),v) for all v such th... |

1335 | The model checker SPIN
- Holzmann
- 1997
(Show Context)
Citation Context ...ecking Basedon Negative Cycle Detection 97 algorithms solve only the reachability problem and do not admit the complete linear time model checking. A distributed version of the LTL model checker SPIN =-=[16]-=- based on nested depth first search approach has been explored in [2]. Other recent papers attempt to use distributed environment of workstations for parallel symbolic model checking. [15] presents a ... |

1062 | Depth-first search and linear graph algorithms - Tarjan - 1972 |

614 |
An automata-theoretic approach to automatic program verification (preliminary report
- Vardi, Wolper
- 1986
(Show Context)
Citation Context ...e experimental results achieved. 2 Automata Based LTL Model Checking Automata based approach to model checking of linear temporal logic formulas is a very elegant method developed by Vardi and Wolper =-=[26]-=-. The essence of using automata for model checking is that both the modelled system and the specification the system is supposed to fulfil are represented in the same way — as Büchi automata. Definiti... |

73 | Distributed-Memory Model Checking with SPIN
- Lerda, Sisto
- 1999
(Show Context)
Citation Context ...hed states is partitioned over the nodes of the parallel machine and the explicit state enumeration is performed in parallel. A similar approach to distributed reachability analysis has been taken in =-=[18]-=-. A distributed version of the UPPAAL model checker based on the same idea as parallel Murϕ has been reported in [3]. Yet another distributed reachability algorithm has been proposed in [1], but has n... |

62 | Parallelizing the murϕ verifier
- Stern, Dill
- 1997
(Show Context)
Citation Context ...come this barrier have been proposed and successfully implemented in automatic verification tools. Recently, some attempts to use multiprocessors and networks of workstations have been undertaken. In =-=[23]-=- the authors describe a parallel version of the verifier Murϕ. The table of all reached states is partitioned over the nodes of the parallel machine and the explicit state enumeration is performed in ... |

53 | Achieving Scalability in Parallel Reachability Analysis of Very Large Circuits - Heyman, Geist, et al. - 2000 |

48 | Negative-cycle detection algorithms
- Cherkassky, Goldberg
- 1999
(Show Context)
Citation Context ...f graphs are known, see i.e. [22]. However, the adjacency matrix representation is not compatible with other space-saving techniques like on-the-fly search. Other algorithms (for excellent survey see =-=[8]-=-), which are based on relaxation of graph’s edges, are inherently sequential and their parallel versions are known only for special settings of the problem. For general digraphs with non-negative edge... |

47 | Distributing timed model checking - how the search order matters - Behrmann, Hune, et al. - 2000 |

45 | Distributed LTL model checking in SPIN - Barnat, Brim, et al. - 2001 |

33 |
Efficient parallel shortest-paths in digraphs with a separator decomposition
- Cohen
- 1993
(Show Context)
Citation Context ...em. For general digraphs with non-negative edge lengths parallel algorithms are presented in [19,20,12]. For special cases of graphs, like planar digraphs [25,13], graphs with separator decomposition =-=[10]-=- or graphs with small tree-width [7] more efficient algorithms are known. Yet none of these algorithms is applicable on directed graphs with potential negative cycles. We present a scalable distribute... |

29 | Scalable distributed onthe-fly symbolic model checking
- Ben-David, Heyman, et al.
- 1954
(Show Context)
Citation Context ...n [2]. Other recent papers attempt to use distributed environment of workstations for parallel symbolic model checking. [15] presents a parallel reachability analysis algorithm based on BDDs while in =-=[4]-=- distributed symbolic method has been applied to check safety RCTL properties. Papers [14,5] significantly extend the scope of properties that can be verified by presenting distributed symbolic model ... |

27 | Parallelizing Dijkstra’s shortest path algorithm - Crauser, Mehlhorn, et al. - 1998 |

22 |
On Firiding and Updating Shortest Paths Distributively
- Venkatesan
- 1992
(Show Context)
Citation Context ...ges, are inherently sequential and their parallel versions are known only for special settings of the problem. For general digraphs with non-negative edge lengths parallel algorithms are presented in =-=[19,20,12]-=-. For special cases of graphs, like planar digraphs [25,13], graphs with separator decomposition [10] or graphs with small tree-width [7] more efficient algorithms are known. Yet none of these algorit... |

21 |
Parallel processing and parallel algorithms: theory and computation
- Roosta
- 2000
(Show Context)
Citation Context ...tive cycles is closely related to the single-source shortest path (SSSP) problem. For this problem effective PRAM algorithms working with adjacency matrix representation of graphs are known, see i.e. =-=[22]-=-. However, the adjacency matrix representation is not compatible with other space-saving techniques like on-the-fly search. Other algorithms (for excellent survey see [8]), which are based on relaxati... |

18 | A simple parallel algorithm for the single-source shortest path problem on planar digraphs
- Träff, Zaroliagis
- 1996
(Show Context)
Citation Context ... known only for special settings of the problem. For general digraphs with non-negative edge lengths parallel algorithms are presented in [19,20,12]. For special cases of graphs, like planar digraphs =-=[25,13]-=-, graphs with separator decomposition [10] or graphs with small tree-width [7] more efficient algorithms are known. Yet none of these algorithms is applicable on directed graphs with potential negativ... |

17 | Progress on the state explosion problem in model checking - Clarke, Grumberg, et al. - 2001 |

15 | Distributed reachability analysis for protocol verification environments - Aggarwal, Alonso, et al. - 1987 |

14 |
Shortest Path Queries in Digraphs of Small Treewidth
- Chaudhuri, Zaroliagis
(Show Context)
Citation Context ...ative edge lengths parallel algorithms are presented in [19,20,12]. For special cases of graphs, like planar digraphs [25,13], graphs with separator decomposition [10] or graphs with small tree-width =-=[7]-=- more efficient algorithms are known. Yet none of these algorithms is applicable on directed graphs with potential negative cycles. We present a scalable distributed algorithm for the negative cycle p... |

11 |
Efficient Sequential and Parallel Algorithms for the Negative Cycle
- Kavvadias, Pantziou, et al.
(Show Context)
Citation Context ... known only for special settings of the problem. For general digraphs with non-negative edge lengths parallel algorithms are presented in [19,20,12]. For special cases of graphs, like planar digraphs =-=[25,13]-=-, graphs with separator decomposition [10] or graphs with small tree-width [7] more efficient algorithms are known. Yet none of these algorithms is applicable on directed graphs with potential negativ... |

11 | Parallel shortest path for arbitrary graphs
- Sanders
- 2000
(Show Context)
Citation Context ...ges, are inherently sequential and their parallel versions are known only for special settings of the problem. For general digraphs with non-negative edge lengths parallel algorithms are presented in =-=[19,20,12]-=-. For special cases of graphs, like planar digraphs [25,13], graphs with separator decomposition [10] or graphs with small tree-width [7] more efficient algorithms are known. Yet none of these algorit... |

9 |
Depth-first search is inherrently sequential
- Reif
- 1985
(Show Context)
Citation Context ...ribute the given graph onto several processors (computers) and to perform a distributed computation. As depth first search is P-complete, promising parallel DFS-based algorithms are unlikely to exist =-=[21]-=-. A completely different approach to distributed emptiness problem is needed. This paper demonstrates the methodology of reducing the automata based LTL model checking problem to the negative cycle de... |

8 | Parallelizing the Mur' veri - Stern, Dill - 1997 |

5 |
Parallel model checking for the alternation free mu-calculus
- Bollig, Leucker, et al.
- 2001
(Show Context)
Citation Context ...allel symbolic model checking. [15] presents a parallel reachability analysis algorithm based on BDDs while in [4] distributed symbolic method has been applied to check safety RCTL properties. Papers =-=[14,5]-=- significantly extend the scope of properties that can be verified by presenting distributed symbolic model checking for µ-calculus and alternation free µ-calculus. In automata based LTL model checkin... |

4 | Distributed shortest path for directed graphs with negative edge lengths - Brim, Černá, et al. - 2001 |

4 | On nested depth search - Holzmann, Peled, et al. - 1996 |

3 | Scalable distributed on-the- symbolic model checking - Ben-David, Heyman, et al. - 2000 |

2 |
Depth first search andlinear graph algorithms
- Tarjan
- 1972
(Show Context)
Citation Context ... and containing an accepting state in the graph corresponding to the Büchi automaton. The best known algorithm for finding cycles in directed graphs is the Tarjan’s depth first search algorithm (DFS) =-=[24]-=-. The practical limitation of this algorithm is the amount of the randomly accessed memory which the algorithm requires. A space efficient alternative to Tarjan’s algorithm (so called nested DFS) allo... |

1 | Distributed model checking for mucalculus - Grumberg, Heyman, et al. - 2001 |

1 |
Courcoubetis. Distributedreachability analysis for protocol verification environments
- Aggarwal, Alonso, et al.
- 1987
(Show Context)
Citation Context ... taken in [18]. A distributed version of the UPPAAL model checker based on the same idea as parallel Murϕ has been reported in [3]. Yet another distributed reachability algorithm has been proposed in =-=[1]-=-, but has not been implemented. We stress that all mentioned ⋆ This work has been partially supportedby the Grant Agency of Czech Republic grants No. 201/00/1023 and201/00/0400. R. Hariharan, M. Mukun... |

1 |
DistributedLTL Model-Checking in SPIN
- Stˇríbrná
- 2001
(Show Context)
Citation Context ...eachability problem and do not admit the complete linear time model checking. A distributed version of the LTL model checker SPIN [16] based on nested depth first search approach has been explored in =-=[2]-=-. Other recent papers attempt to use distributed environment of workstations for parallel symbolic model checking. [15] presents a parallel reachability analysis algorithm based on BDDs while in [4] d... |

1 |
Distributedtimedmodel checking — how the search order matters
- Vaandrager
- 2000
(Show Context)
Citation Context ...arallel. A similar approach to distributed reachability analysis has been taken in [18]. A distributed version of the UPPAAL model checker based on the same idea as parallel Murϕ has been reported in =-=[3]-=-. Yet another distributed reachability algorithm has been proposed in [1], but has not been implemented. We stress that all mentioned ⋆ This work has been partially supportedby the Grant Agency of Cze... |

1 |
Distributedshortest path for directed graphs with negative edge lengths
- Pelánek
- 2001
(Show Context)
Citation Context ... G is distributed over P processors each of which owns O(n/P ) vertices, then the worst case computation complexity is O(n3 /P ). For detailed proof of the correctness and the complexity analysis see =-=[6]-=-. 5 Experiments We have implemented the algorithm proposed in Section 4. The implementation has been done in C++ and the experiments have been performed on a cluster of eight 366 MHz Pentium PC Linux ... |

1 |
Progress on the state explosion problem in model checking
- Veith
- 2001
(Show Context)
Citation Context ...fication problems is the real computational power available (time and especially memory). Therefore verification of complex concurrent systems requires techniques to avoid the state-explosion problem =-=[9]-=-. Several sequential methods (partial order reductions, on-the-fly search) to overcome this barrier have been proposed and successfully implemented in automatic verification tools. Recently, some atte... |

1 |
A parallelization of Dijkstra’s shortest path algorithm
- Sanders
(Show Context)
Citation Context ...ges, are inherently sequential and their parallel versions are known only for special settings of the problem. For general digraphs with non-negative edge lengths parallel algorithms are presented in =-=[19,20,12]-=-. For special cases of graphs, like planar digraphs [25,13], graphs with separator decomposition [10] or graphs with small tree-width [7] more efficient algorithms are known. Yet none of these algorit... |

1 |
Distributedmodel checking for mucalculus
- Schuster
- 2001
(Show Context)
Citation Context ...allel symbolic model checking. [15] presents a parallel reachability analysis algorithm based on BDDs while in [4] distributed symbolic method has been applied to check safety RCTL properties. Papers =-=[14,5]-=- significantly extend the scope of properties that can be verified by presenting distributed symbolic model checking for µ-calculus and alternation free µ-calculus. In automata based LTL model checkin... |

1 |
Achieving scalability in parallel reachability analysis of very large circuits
- Schuster
- 2000
(Show Context)
Citation Context ...hecker SPIN [16] based on nested depth first search approach has been explored in [2]. Other recent papers attempt to use distributed environment of workstations for parallel symbolic model checking. =-=[15]-=- presents a parallel reachability analysis algorithm based on BDDs while in [4] distributed symbolic method has been applied to check safety RCTL properties. Papers [14,5] significantly extend the sco... |

1 |
On nesteddepth first search
- Yannakakis
- 1996
(Show Context)
Citation Context ...y accessed memory which the algorithm requires. A space efficient alternative to Tarjan’s algorithm (so called nested DFS) allowing to optimise the amount of randomly accessed memory exists (see i.e. =-=[17]-=-) and is implemented in SPIN verification tool [16]. However, even this optimisation does not solve the state space explosion problem sufficiently. A very natural way how to overcome the memory limita... |