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## On-the-fly Emptiness Checks for Generalized Büchi Automata (2005)

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Venue: | IN PROC. 12TH INTL. SPIN WORKS. ON MODEL CHECKING SOFTWARE, LNCS #1708 |

Citations: | 27 - 10 self |

### Citations

475 |
The SPIN Model Checker
- Holzmann
- 1997
(Show Context)
Citation Context ...ty graph (i.e., without partial order reduction—the conclusion for the reduced graphs are similar, only with smaller figures) of the model has been generated from its Promela specification using Spin =-=[13]-=-. Then the corresponding TGBA has been introduced in Spot and the formulæ translated into TGBAs using also Spot. Though this is not generally the case, on this example the sizes of the degeneralized p... |

291 | An automata-theoretic approach to linear temporal logic
- Vardi
- 1995
(Show Context)
Citation Context ...heuristics to improve existing checks, and propose algorithms to compute accepting runs in the case of multiple acceptance conditions. 1 Introduction The automata-theoretic approach to model-checking =-=[22]-=- uses automata on infinite words to represent a system as well as a formula to check on this system. Both automata are synchronized, and a key operation is to determine whether the resulting automaton... |

259 | A.: Checking that Finite State Concurrent Programs Satisfy their Linear Specification
- Lichtenstein, Pnueli
- 1985
(Show Context)
Citation Context ... 2005 [12] Truly On−The−Fly LTL Model Checking Hammer et al., 2005 Depth−first search and linear graph algorithms Tarjan, 1972 Finding the maximum strong components in a directed graph Dijkstra, 1973 =-=[16]-=- Checking That Finite State Concurrent Programs Satisfy Their Linear Specification Lichtenstein and Pnueli, 1985 [3] On−the−fly Verification of Linear Temporal Logic Couvreur, 1999 [20] Nested Emptine... |

177 | Property specification patterns for finite-state verification
- Dwyer, Avrunin, et al.
- 1998
(Show Context)
Citation Context ...g the algorithm of Couvreur [3]), yielding 3000 different products. On setups with “Humangenerated formulæ”, each graph is checked against 94 formulæ (and their negation) selected from the literature =-=[5, 6, 18]-=-, yielding 2820 products. In this first test we discarded all products without accepting run (i.e., keeping those where algorithms need not visit the whole automaton). For each setup the number of non... |

89 | M.: Memory-Efficient Algorithms for the Verification of Temporal Properties
- Courcoubetis, Vardi, et al.
- 1992
(Show Context)
Citation Context ...jan’s Algorithm Makes On−the−Fly LTL Verification More Efficient Geldenhuys & Valmari, 2004 [9] More Efficient On−the−fly LTL Verification with Tarjan’s Algorithm Geldenhuys & Valmari, 2005 Cou99 shy =-=[2]-=- Memory−Efficient Algorithms for the Verification of Temporal Properties Courcoubetis et al., 1990 [11] On the Verification of Temporal Properties Godefroid & Holzmann, 1993 [14] On Nested Depth First... |

88 | On nested depth first search
- GJ, Peled, et al.
- 1996
(Show Context)
Citation Context ...almari, 2005 Cou99 shy [2] Memory−Efficient Algorithms for the Verification of Temporal Properties Courcoubetis et al., 1990 [11] On the Verification of Temporal Properties Godefroid & Holzmann, 1993 =-=[14]-=- On Nested Depth First Search Holzmann et al., 1996 This paper Legend: Büchi automata with accepting states Generalized Büchi automata with accepting states Generalized Buchï automata with accepting t... |

72 | Optimizing Büchi automata
- Etessami, Holzmann
(Show Context)
Citation Context ...g the algorithm of Couvreur [3]), yielding 3000 different products. On setups with “Humangenerated formulæ”, each graph is checked against 94 formulæ (and their negation) selected from the literature =-=[5, 6, 18]-=-, yielding 2820 products. In this first test we discarded all products without accepting run (i.e., keeping those where algorithms need not visit the whole automaton). For each setup the number of non... |

50 | SPOT: An extensible model checking library using transition-based generalized büchi automata
- Duret-Lutz, Poitrenaud
- 2004
(Show Context)
Citation Context ...ns In this section we introduce the experimental framework in which we compare the aforementioned algorithms, and comment on the results. All the algorithms we use are implemented in the Spot library =-=[4]-=-. The random graph and random LTL formulæ generation algorithms are comparable to those presented by Tauriainen [21]. Of the 8 emptiness-check algorithms we compare, the first 4 are SCC-based: Cou99, ... |

38 | On the veri of temporal properties
- Godefroid, Holzmann
- 1993
(Show Context)
Citation Context ...fficient On−the−fly LTL Verification with Tarjan’s Algorithm Geldenhuys & Valmari, 2005 Cou99 shy [2] Memory−Efficient Algorithms for the Verification of Temporal Properties Courcoubetis et al., 1990 =-=[11]-=- On the Verification of Temporal Properties Godefroid & Holzmann, 1993 [14] On Nested Depth First Search Holzmann et al., 1996 This paper Legend: Büchi automata with accepting states Generalized Büchi... |

36 | From states to transitions: Improving translation of LTL formulæ to Büchi automata
- Giannakopoulou, Lerda
- 2002
(Show Context)
Citation Context ...ave acceptance conditions on states rather than transitions, and are often not generalized (i.e., |F| � 1). While the benefit of TGBAs in the process of translating LTL formulæ is already quite clear =-=[3, 10, 4]-=-, few people are actually using them for emptiness-check, because mainstream algorithms work on non-generalized, state-based, Büchi automata. A degeneralization is the transformation of an automaton w... |

34 | A note on on-the-fly verification algorithms
- Schwoon, Esparza
- 2005
(Show Context)
Citation Context ...onized automata to be constructed lazily while it runs. This is a win if the emptiness check answers before the whole synchronized product is completed. We follow up on a paper by Schwoon and Esparza =-=[17]-=- who compared two classes of on-the-fly emptiness checks: those based on nested depth-first searches (NDFSs) versus those computing strongly connected components (SCCs). Their measures for Büchi autom... |

17 | Truly on-the-fly LTL model checking
- Hammer, Merz, et al.
- 2005
(Show Context)
Citation Context ...earches (NDFSs), and algorithms that compute strongly connected components (SCCs). Fig. 1 shows how the algorithms we cite relate to each other.s1972 1973 1985 1990 1993 1994 1996 1999 2003 2004 2005 =-=[12]-=- Truly On−The−Fly LTL Model Checking Hammer et al., 2005 Depth−first search and linear graph algorithms Tarjan, 1972 Finding the maximum strong components in a directed graph Dijkstra, 1973 [16] Check... |

16 |
On-the-fly verification of temporal logic
- Couvreur
- 1999
(Show Context)
Citation Context ...th-first searches (NDFSs) versus those computing strongly connected components (SCCs). Their measures for Büchi automata with single acceptance conditions led to the following conclusions: – Couvreur =-=[3]-=-’s algorithm is the best at computing accepting SCCs, – Schwoon and Esparza [17]’s algorithm is the best of NDFS-based checks, – for weak Büchi automata [1], a simple DFS is enough; otherwise SCC-base... |

16 | Minimization of counterexamples in SPIN
- Gastin, Moro, et al.
- 2004
(Show Context)
Citation Context ...Depth First Search Holzmann et al., 1996 This paper Legend: Büchi automata with accepting states Generalized Büchi automata with accepting states Generalized Buchï automata with accepting transitions =-=[7]-=- Minimization of counterexamples in SPIN Gastin et al., 2004 An Improvement in Formal Verification Holzmann & Peled, 1994 [19] On Translating LTL into Alternating and Nondeterministic Automata Tauriai... |

15 | R.: Relating hierarchy of temporal properties to model checking
- Černá, Pelánek
- 2003
(Show Context)
Citation Context ...ed to the following conclusions: – Couvreur [3]’s algorithm is the best at computing accepting SCCs, – Schwoon and Esparza [17]’s algorithm is the best of NDFS-based checks, – for weak Büchi automata =-=[1]-=-, a simple DFS is enough; otherwise SCC-based algorithms should be preferred to NDFSs unless bit-state hashing is used. Here we explore these algorithms on Büchi automata with multiple acceptance cond... |

15 |
More efficient on-the-fly LTL verification with Tarjan’s algorithm
- Geldenhuys, Valmari
(Show Context)
Citation Context ...n degeneralized automata, exhibiting an accepting run if one exists is straightforward. In NDFS-based algorithms (CVWY90, SE05) that run is the contents of the stack. For GV04, Geldenhuys and Valmari =-=[9]-=- showed how to use an extra integer per stack state to produce an accepting run. t1st1 // Let 〈Σ, Q, δ, q 0 , F〉 be the t2 // input automaton to check. t3 H: map of Q ↦→ 〈color ∈ {cyan, blue}, t4 acc ... |

13 | Coping With Strong Fairness
- Latvala, Heljanko
- 2000
(Show Context)
Citation Context ... conditions F1 that intersect F1. Iterate until Fn = ∅. Finally use a last BFS to compute the shortest path from cn back to c0, closing the cycle. This algorithm was presented by Latvala and Heljanko =-=[15]-=- using the root of the SCC as c0. However the choice of c0 can be arbitrary because we are in a SCC. Since we know that the transition that caused Cou99 to exit (the one corresponding to the last exec... |

11 |
Tarjan’s Algorithm Makes On-the-Fly LTL Verification More Efficient
- Geldenhuys, Valmari
- 2004
(Show Context)
Citation Context ...ent Programs Satisfy Their Linear Specification Lichtenstein and Pnueli, 1985 [3] On−the−fly Verification of Linear Temporal Logic Couvreur, 1999 [20] Nested Emptiness Search for GBA Tauriainen, 2003 =-=[8]-=- Tarjan’s Algorithm Makes On−the−Fly LTL Verification More Efficient Geldenhuys & Valmari, 2004 [9] More Efficient On−the−fly LTL Verification with Tarjan’s Algorithm Geldenhuys & Valmari, 2005 Cou99 ... |

9 | Nested emptiness search for generalized buchi automata
- Tauriainen
- 2004
(Show Context)
Citation Context ...done carefully. The bit-state hashing should not be applied to states that belong to the first-level DFS: those states need to be perfectly hashed. The application to Tau03 is discussed by Tauriainen =-=[20]-=-. In SCC-based algorithms the restriction extends to all states that belong to SCCs in the SCC stack. In other words, bit-state hashing can only be applied to states from removed MSCCs; this limits it... |

8 | A Randomized Testbench for Algorithms Translating Linear Temporal Logic Formulae into Büchi Automata
- Tauriainen
- 1999
(Show Context)
Citation Context ...omment on the results. All the algorithms we use are implemented in the Spot library [4]. The random graph and random LTL formulæ generation algorithms are comparable to those presented by Tauriainen =-=[21]-=-. Of the 8 emptiness-check algorithms we compare, the first 4 are SCC-based: Cou99, is the algorithm of Fig. 2, Cou99 shy- and Cou99 shy are two variants of Cou99 described in Section 4.1, and GV04 is... |

7 | On translating linear temporal logic into alternating and nondeterministic automata
- Tauriainen
- 2003
(Show Context)
Citation Context ...ith accepting states Generalized Buchï automata with accepting transitions [7] Minimization of counterexamples in SPIN Gastin et al., 2004 An Improvement in Formal Verification Holzmann & Peled, 1994 =-=[19]-=- On Translating LTL into Alternating and Nondeterministic Automata Tauriainen, 2003 Tau03 opt Fig. 1. A family tree of emptiness-check algorithms. [17] A Note on On−The−Fly Verification Algorithms Sch... |

6 |
Efficient Büchi automata for LTL formulæ
- Somenzi, Bloem
- 2000
(Show Context)
Citation Context ...g the algorithm of Couvreur [3]), yielding 3000 different products. On setups with “Humangenerated formulæ”, each graph is checked against 94 formulæ (and their negation) selected from the literature =-=[5, 6, 18]-=-, yielding 2820 products. In this first test we discarded all products without accepting run (i.e., keeping those where algorithms need not visit the whole automaton). For each setup the number of non... |

1 |
Tarjan’s algorithm makes on-the-flyLTLverification more efficient
- Geldenhuys, Valmari
- 2004
(Show Context)
Citation Context ...ent Programs Satisfy Their Linear Specification Lichtenstein and Pnueli, 1985 [3] On−the−fly Verification of Linear Temporal Logic Couvreur, 1999 [20] Nested Emptiness Search for GBA Tauriainen, 2003 =-=[8]-=- Tarjan’s Algorithm Makes On−the−Fly LTL Verification More Efficient Geldenhuys & Valmari, 2004 [9] More Efficient On−the−fly LTL Verification with Tarjan’s Algorithm Geldenhuys & Valmari, 2005 Cou99 ... |

1 |
A note on on-the-flyverification algorithms
- Schwoon, Esparza
- 2005
(Show Context)
Citation Context ...onized automata to be constructed lazily while it runs. This is a win if the emptiness check answers before the whole synchronized product is completed. We follow up on a paper by Schwoon and Esparza =-=[17]-=- who compared two classes of on-the-fly emptiness checks: those based on nested depth-first searches (NDFSs) versus those computing strongly connected components (SCCs). Their measures for Büchi autom... |