## Regular model checking without transducers (2006)

Citations: | 23 - 12 self |

### BibTeX

@TECHREPORT{Abdulla06regularmodel,

author = {Parosh Aziz Abdulla and Giorgio Delzanno and Noomene Ben Henda and Ahmed Rezine},

title = {Regular model checking without transducers},

institution = {},

year = {2006}

}

### OpenURL

### Abstract

Abstract. We give a simple and efficient method to prove safety properties for parameterized systems with linear topologies. A process in the system is a finite-state automaton, where the transitions are guarded by both local and global conditions. Processes may communicate via broadcast, rendez-vous and shared variables. The method derives an overapproximation of the induced transition system, which allows the use of a simple class of regular expressions as a symbolic representation. Compared to traditional regular model checking methods, the analysis does not require the manipulation of transducers, and hence its simplicity and efficiency. We have implemented a prototype which works well on several mutual exclusion algorithms and cache coherence protocols. 1

### Citations

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Citation Context ...defined as follows: PAR-COV Instance – A parameterized system P = (Q, X, T ). – An upward closed set CF of configurations. ∗ Question Init −→ CF ? It can be shown, using standard techniques (see e.g. =-=[28, 16]-=-), that checking safety properties (expressed as regular languages) can be translated into instances of the coverability problem. Therefore, checking safety properties amounts to solving PAR-COV(i.e.,... |

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Citation Context ...ly discarded in the algorithm. An aspect of our constraint system is that each constraint characterizes a set of configurations which is upward closed with respect to ≼. Conversely (by Higman’s Lemma =-=[17]-=-), any upward closed set CF of configurations can be characterized as [ΦF ] where ΦF is a finite set of constraints. In this manner, APRXPAR-COV is reduced to checking the reachability of a finite set... |

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Citation Context ...defined as follows: PAR-COV Instance – A parameterized system P = (Q, X, T ). – An upward closed set CF of configurations. ∗ Question Init −→ CF ? It can be shown, using standard techniques (see e.g. =-=[28, 16]-=-), that checking safety properties (expressed as regular languages) can be translated into instances of the coverability problem. Therefore, checking safety properties amounts to solving PAR-COV(i.e.,... |

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Citation Context ...gular languages. A technique of particular interest for parameterized systems is that of counter abstraction. The idea is to keep track of the number of processes which satisfy a certain property. In =-=[15]-=- the technique generates an abstract system which is essentially a Petri net. Counter abstracted models with broadcast communication are proved to be well-structured in [14]. In [10, 11] symbolic mode... |

127 | Regular model checking
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Citation Context ...work Several recent works have been devoted to develop regular model checking, e.g., [19, 9]; and in particular augmenting regular model checking with techniques such as widening [6, 27], abstraction =-=[7]-=-, and acceleration [3]. All these works rely on computing the transitive closure of transducers or on iterating them on regular languages. A technique of particular interest for parameterized systems ... |

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Citation Context ...source of approximation in the model. Since the approximate transition relation is monotonic, it can be analyzed using symbolic backward reachability algorithm based on a generic method introduced in =-=[1]-=-. An attractive feature of this algorithm is that it operates on sets of configurations which are upward closed with respect to the subword relation. In particular, reachability analysis can be perfor... |

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Citation Context ...hms, bus protocols, telecommunication protocols, and cache coherence protocols. One important technique which has been used for verification of parameterized systems is that of regular model checking =-=[19, 3, 6]-=-. In regular model checking, states are represented by words, sets of states by regular expressions, and transitions by finite automata operating on pairs of states, so called finite-state transducers... |

73 | Automatic deductive verification with invisible invariants
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Citation Context ... hardware systems using the monadic second-order logic on strings. Other parameterized verification methods are based on reductions to finitestate models. Among these, the invisible invariants method =-=[4, 23]-=- exploits cutoff properties to check invariants for mutual exclusion protocols like the Bakery algorithm and German’s protocol. The success of the method depends on the heuristic used in the generatio... |

66 | On the verification of broadcast protocols
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Citation Context ...sfy a certain property. In [15] the technique generates an abstract system which is essentially a Petri net. Counter abstracted models with broadcast communication are proved to be well-structured in =-=[14]-=-. In [10, 11] symbolic model checking based on real arithmetics is used to verify counter abstracted models of cache coherence protocols enriched with global conditions. The method works without guara... |

45 | Indexed predicate discovery for unbounded system verification
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Citation Context ... using the weakest precondition operator. The method requires the user to provide a set of predicates on which to compute the abstract model. Heuristics to discover indexed predicates are proposed in =-=[20]-=- and applied to German’s protocol as well as to the Bakery algorithm. In contrast to these approaches, we provide a uniform approximation scheme which is independent on the analyzed system. Environmen... |

43 | Undecidable problems in unreliable computations
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Citation Context ...g (in the original model) by resetting the counter value to zero (in the approximate model). Thus, we are essentially approximating the counter machine by the corresponding lossy counter machine (see =-=[22]-=- for a description of lossy counter machines). In fact, we can equivalently add counters as a separate feature (without simulation through universal conditions), and approximate zero-testing by resett... |

26 |
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Citation Context ...hms, bus protocols, telecommunication protocols, and cache coherence protocols. One important technique which has been used for verification of parameterized systems is that of regular model checking =-=[19, 3, 6]-=-. In regular model checking, states are represented by words, sets of states by regular expressions, and transitions by finite automata operating on pairs of states, so called finite-state transducers... |

25 | Exact and efficient verification of parameterized cache coherence protocols
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(Show Context)
Citation Context ... as broadcast communication, rendez-vous communication, and dynamic behaviour. Other approaches tailored to snoopy cache protocols mod-eled with broadcast communication are presented in [13, 21]. In =-=[12]-=- German’s directory-based protocol is verified via a manual transformation into a snoopy protocol. It is important to remark that frameworks for finite-state abstractions [8] and those based on cutoff... |

23 | MOSEL: A flexible toolset for monadic second-order logic
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Citation Context ...architectures. Our method can cope with this kind of systems, since unstructured architectures can be viewed as a special case of linear arrays where the ordering of the processes is not relevant. In =-=[18]-=- and [26], the authors present a tool for the analysis and the verification of linear parameterized hardware systems using the monadic second-order logic on strings. Other parameterized verification m... |

22 | Regular model checking made simple and efficient
- Abdulla, Jonsson, et al.
- 2002
(Show Context)
Citation Context ...hms, bus protocols, telecommunication protocols, and cache coherence protocols. One important technique which has been used for verification of parameterized systems is that of regular model checking =-=[19, 3, 6]-=-. In regular model checking, states are represented by words, sets of states by regular expressions, and transitions by finite automata operating on pairs of states, so called finite-state transducers... |

21 | Iterating transducers
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(Show Context)
Citation Context ...gorithms, the Java Meta-locking protocol, the Futurebus+ protocol, German’s directory-based protocol, etc. Related work Several recent works have been devoted to develop regular model checking, e.g., =-=[19, 9]-=-; and in particular augmenting regular model checking with techniques such as widening [6, 27], abstraction [7], and acceleration [3]. All these works rely on computing the transitive closure of trans... |

20 |
Liveness with (0, 1,infinity)-counter abstraction
- Pnueli, Xu, et al.
- 2002
(Show Context)
Citation Context ...ecking based on real arithmetics is used to verify counter abstracted models of cache coherence protocols enriched with global conditions. The method works without guarantee of termination. The paper =-=[24]-=- refines the counter abstraction idea by truncating the counters at the value of 2, and thus obtains a finite-state abstract system. The method may require manual insertion of auxiliary program variab... |

19 | Environment abstraction for parameterized verification
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- 2006
(Show Context)
Citation Context ...o German’s protocol as well as to the Bakery algorithm. In contrast to these approaches, we provide a uniform approximation scheme which is independent on the analyzed system. Environment abstraction =-=[8]-=- combines predicate abstraction with the counter abstraction. The technique is applied to the Bakery and Szymanski algorithms. The model of [8] contains a more restricted form of global conditions tha... |

18 |
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(Show Context)
Citation Context ...features such as broadcast communication, rendez-vous communication, and dynamic behaviour. Other approaches tailored to snoopy cache protocols mod-eled with broadcast communication are presented in =-=[13, 21]-=-. In [12] German’s directory-based protocol is verified via a manual transformation into a snoopy protocol. It is important to remark that frameworks for finite-state abstractions [8] and those based ... |

17 |
Parameterized Verification of a Cache Coherence Protocol: Safety and Liveness
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Citation Context ...s on the heuristic used in the generation of the candidate invariant. This method sometimes (e.g. for German’s protocol) requires insertion of auxiliary program variables for completing the proof. In =-=[5]-=- finite-state abstractions for verification of systems specified in WS1S are computed on-the-fly by using the weakest precondition operator. The method requires the user to provide a set of predicates... |

17 |
Regular Model Checking using Widening Techniques
- Touili
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Citation Context ...otocol, etc. Related work Several recent works have been devoted to develop regular model checking, e.g., [19, 9]; and in particular augmenting regular model checking with techniques such as widening =-=[6, 27]-=-, abstraction [7], and acceleration [3]. All these works rely on computing the transitive closure of transducers or on iterating them on regular languages. A technique of particular interest for param... |

12 | A unifying model checking approach for safety properties of parameterized systems
- Maidl
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Citation Context ...features such as broadcast communication, rendez-vous communication, and dynamic behaviour. Other approaches tailored to snoopy cache protocols mod-eled with broadcast communication are presented in =-=[13, 21]-=-. In [12] German’s directory-based protocol is verified via a manual transformation into a snoopy protocol. It is important to remark that frameworks for finite-state abstractions [8] and those based ... |

11 |
Automated verification of cache coherence protocols
- Delzanno
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(Show Context)
Citation Context ...tain property. In [15] the technique generates an abstract system which is essentially a Petri net. Counter abstracted models with broadcast communication are proved to be well-structured in [14]. In =-=[10, 11]-=- symbolic model checking based on real arithmetics is used to verify counter abstracted models of cache coherence protocols enriched with global conditions. The method works without guarantee of termi... |

9 | Verification of consistency protocols via infinite-state symbolic model checking
- Delzanno
(Show Context)
Citation Context ...tain property. In [15] the technique generates an abstract system which is essentially a Petri net. Counter abstracted models with broadcast communication are proved to be well-structured in [14]. In =-=[10, 11]-=- symbolic model checking based on real arithmetics is used to verify counter abstracted models of cache coherence protocols enriched with global conditions. The method works without guarantee of termi... |

9 | Automated inductive verification of parameterized protocols
- Roychoudhury, Ramakrishnan
- 2001
(Show Context)
Citation Context ...h component itself contains counters and other unbounded data structures. This allows for instance to deal with a model of the Bakery algorithm which is more concrete (precise) than ours. Finally, in =-=[25]-=- a parameterized version of the Java Meta-locking algorithm is verified by means of an induction-based proof technique which requires manual strengthening of the mutual exclusion invariant. In summary... |

4 |
B.: jMosel: A stand-alone tool and jABC plugin for M2L(Str
- Wilhelm, Margaria, et al.
- 2006
(Show Context)
Citation Context ...ures. Our method can cope with this kind of systems, since unstructured architectures can be viewed as a special case of linear arrays where the ordering of the processes is not relevant. In [18] and =-=[26]-=-, the authors present a tool for the analysis and the verification of linear parameterized hardware systems using the monadic second-order logic on strings. Other parameterized verification methods ar... |