## Model-Checking for a Subclass of Event Structures (1997)

Venue: | Proc. of TACAS'97, LNCS 1217 |

Citations: | 15 - 8 self |

### BibTeX

@INPROCEEDINGS{Penczek97model-checkingfor,

author = {Wojciech Penczek},

title = {Model-Checking for a Subclass of Event Structures},

booktitle = {Proc. of TACAS'97, LNCS 1217},

year = {1997},

pages = {145--164},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. A finite representation of the prime event structure corresponding to the behaviour of a program is suggested. The algorithm of linear complexity using this representation for model checking of the formulas of Discrete Event Structure Logic without past modalities is given. A method of building finite representations of event structures in an efficient way by applying partial order reductions is provided. 1 Introduction Model checking is one of the most successful methods of automatic verification of program properties. A model-checking algorithm decides whether a finite-state concurrent system satisfies its specification, given as a formula of a temporal logic [3, 10]. Behaviour of a concurrent system can be modeled in two ways. In the interleaving semantics, the meaning of a program is an execution tree, temporal-logic assertions are interpreted over paths of this tree. In partial-order semantics (or event structure semantics), behaviour is an event structure, where the ordering r...

### Citations

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(Show Context)
Citation Context ...theory. In this framework, a concurrent system P , possibly with fairness requirements, is a Kripke structure MP that generates the execution tree. The commonly employed specification language is CTL =-=[3, 6]-=-. To check whether the structure MP satisfies a CTL-formula ', the model-checking algorithm assigns the subformulas of ' to states of MP ; if the beginning state has been assigned the formula ', then ... |

989 | Depth first search and linear graph algorithms
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Citation Context ...ates [ ] ES of F TS by the values of the function f of their representatives, i.e., f( ). Note that FTS can be directly generated from the given program P using the Depth First Search (DFS)-algorithm =-=[26]-=-. The algorithm starts from the beginning state (g 0 ; t 0 ) and then, recursively, for a current state (g; X) and enabled transition t 2 \Sigma expands the t-successor (g 0 ; X 0 ) of (g; X). When al... |

270 |
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Citation Context ...ethods of automatic verification of program properties. A model-checking algorithm decides whether a finite-state concurrent system satisfies its specification, given as a formula of a temporal logic =-=[3, 10]-=-. Behaviour of a concurrent system can be modeled in two ways. In the interleaving semantics, the meaning of a program is an execution tree, temporal-logic assertions are interpreted over paths of thi... |

263 |
Event structures
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Citation Context ...f this tree. In partial-order semantics (or event structure semantics), behaviour is an event structure, where the ordering relations over events reflect the causal dependency and conflict among them =-=[29]-=-. So far model checking algorithms have been suggested for many partial-order temporal logics [24, 27, 1, 15]. There is a long and rich tradition of research that employs the interleaving semantics, r... |

180 |
editors. The book of traces
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Citation Context ...te g n . Example 1. Program MUTEX is shown in Figure 1. It is composed of three processes, which local states are denoted with circles, whereas the transitions with horizontal bars, e.g. b = ((3; 8); =-=(5; 10)-=-). The program ensures the mutual exclusion of access to the local states 5 and 6 being the critical sections. S 1 = f1; 3; 5g, S 2 = f2; 4; 6g, S 3 = f7; 8; 9; 10; 11g, and s 0 1 = 1, s 0 2 = 2, and ... |

78 |
Basic Notions of Trace Theory, in
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(Show Context)
Citation Context ...sentations. Model checking of DESL is described in section 9 and the discussion can be found in section 10. 2 Event Structures We start with the definitions of event structures [29] and trace systems =-=[12]-=-, which are used for giving semantics to concurrent systems. Let S be a countable set, and let ! be a binary relation over S. The inverse of ! is denoted by ! \Gamma1 . For an element s 2 S, the set #... |

62 | A technique of a state space search based on unfolding
- McMillan
- 1995
(Show Context)
Citation Context ...linear in the number of subformulas of a checked formula. As far as efficient generation of quotient structures of event structures is concerned, it seems possible to apply also net unfolding methods =-=[11]-=-. It is important to mention that for unrestricted programs Lemma 9 OE E ) still holds making it possible to model check the DESL formulas without conflict operators. Moreover our method can be applie... |

54 | A partial order approach to branching time logic model checking
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Citation Context ... definition of MES and Lemma 10. ut 8 Efficient Method of Generating FES The above method of generating FES can be substantially improved for some programs by applying partial order reduction methods =-=[7, 18]-=-. Despite the equivalence classes of not-prime traces (called global states) do not occur in the structure FES , some of them need to be generated in order to establish whether two equivalence classes... |

46 |
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Citation Context ...restricted class of programs in which the conflicting transitions having at least one beginning state in common belong to the same sequential agents. This class of programs is called free-choice (see =-=[4]-=- for the definition for Petri Nets) and it is formally defined as follows: Definition3. A program P is said to be free-choice, if for each two transitions t = (s; s 1 ) 2 \Gamma X ; t 0 = (s 0 ; s 0 1... |

46 |
A trace based extension of linear time temporal logic
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Citation Context ...cture, where the ordering relations over events reflect the causal dependency and conflict among them [29]. So far model checking algorithms have been suggested for many partial-order temporal logics =-=[24, 27, 1, 15]-=-. There is a long and rich tradition of research that employs the interleaving semantics, resulting in both theoretical and practical results. The main reason for this is the simplicity of the model p... |

44 |
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Citation Context ...ethods of automatic verification of program properties. A model-checking algorithm decides whether a finite-state concurrent system satisfies its specification, given as a formula of a temporal logic =-=[3, 10]-=-. Behaviour of a concurrent system can be modeled in two ways. In the interleaving semantics, the meaning of a program is an execution tree, temporal-logic assertions are interpreted over paths of thi... |

43 | Model-checking of causality properties
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(Show Context)
Citation Context ...cture, where the ordering relations over events reflect the causal dependency and conflict among them [29]. So far model checking algorithms have been suggested for many partial-order temporal logics =-=[24, 27, 1, 15]-=-. There is a long and rich tradition of research that employs the interleaving semantics, resulting in both theoretical and practical results. The main reason for this is the simplicity of the model p... |

32 |
A temporal logic for reasoning about partially ordered computations
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Citation Context ...xecutions that are equivalentsup to reordering of independent transitions, thereby, resulting in a more abstract and faithful representation of concurrency [19, 27, 1, 15]. Logics over partial orders =-=[25, 19, 20, 21, 22]-=- allow a direct representation of properties involving causality, conflict, and concurrency. The first temporal logic on prime event structures has been put forward by Lodaya and Thiagarajan [9]. Sinc... |

19 |
P.S.Thiagarajan: Linear Time Temporal Logics over Mazurkiewicz Traces
- Mukund
- 1996
(Show Context)
Citation Context ...cture, where the ordering relations over events reflect the causal dependency and conflict among them [29]. So far model checking algorithms have been suggested for many partial-order temporal logics =-=[24, 27, 1, 15]-=-. There is a long and rich tradition of research that employs the interleaving semantics, resulting in both theoretical and practical results. The main reason for this is the simplicity of the model p... |

18 |
Proving partial order properties
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(Show Context)
Citation Context ... It does not distinguish among total-order executions that are equivalentsup to reordering of independent transitions, thereby, resulting in a more abstract and faithful representation of concurrency =-=[19, 27, 1, 15]-=-. Logics over partial orders [25, 19, 20, 21, 22] allow a direct representation of properties involving causality, conflict, and concurrency. The first temporal logic on prime event structures has bee... |

16 | Temporal logics for trace systems: On automated verification
- Penczek
- 1993
(Show Context)
Citation Context ...xecutions that are equivalentsup to reordering of independent transitions, thereby, resulting in a more abstract and faithful representation of concurrency [19, 27, 1, 15]. Logics over partial orders =-=[25, 19, 20, 21, 22]-=- allow a direct representation of properties involving causality, conflict, and concurrency. The first temporal logic on prime event structures has been put forward by Lodaya and Thiagarajan [9]. Sinc... |

15 |
A modal logic for a subclass of event structures
- Lodaya, Thiagarajan
- 1987
(Show Context)
Citation Context ..., 21, 22] allow a direct representation of properties involving causality, conflict, and concurrency. The first temporal logic on prime event structures has been put forward by Lodaya and Thiagarajan =-=[9]-=-. Since then several new logics on event structures have been defined [20, 21, 13, 14, 23]. Most of these logics have been proved to be decidable and possessing complete axiomatizations. However, the ... |

14 |
A temporal logic for event structures
- Penczek
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(Show Context)
Citation Context ...xecutions that are equivalentsup to reordering of independent transitions, thereby, resulting in a more abstract and faithful representation of concurrency [19, 27, 1, 15]. Logics over partial orders =-=[25, 19, 20, 21, 22]-=- allow a direct representation of properties involving causality, conflict, and concurrency. The first temporal logic on prime event structures has been put forward by Lodaya and Thiagarajan [9]. Sinc... |

13 | Branching Time and Partial Order in Temporal Logics, Time and Logic: A Computational Approach
- Penczek
- 1995
(Show Context)
Citation Context ..., conflict, and concurrency. The first temporal logic on prime event structures has been put forward by Lodaya and Thiagarajan [9]. Since then several new logics on event structures have been defined =-=[20, 21, 13, 14, 23]-=-. Most of these logics have been proved to be decidable and possessing complete axiomatizations. However, the model checking problem for event structure logics has never been addressed. The reason for... |

11 |
Partial order reduction: Model-checking using representatives
- Peled
- 1996
(Show Context)
Citation Context ...ete Event Structure Logic (DESL) [21] without past modalities. We suggest also a method of building finite representations of event structures in an efficient way by applying partial order reductions =-=[18]-=-. This is the first model checking algorithm for an event structure logic suggested in the literature. ? Partially supported by The State Committee for Scientific Research under the grant No. 8 T11C 0... |

10 |
Traces and logic
- Penczek, Kuiper
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(Show Context)
Citation Context |

9 |
A -calculus with local views for systems of sequential agents
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Citation Context ... + 1 ak a 2k\Gamma2 Fig. 7. The global state space contains k 2 states, whereas the reduced structure only 4k \Gamma 4 states, for k \Gamma 1-transitions in each of the two processes. logics: ()TrPTL =-=[15, 16]-=- and TLC [1]. Our algorithm is the first one, which is designed for a logic interpreted on event structures. It is also the first model checking algorithm for a partial order logic, which is linear in... |

9 |
A linear local model checking algorithm for ctl
- Vergauwen, Levi
- 1993
(Show Context)
Citation Context ...o perform model checking over the structure R TS itself. Our method relies on translating DESL causality formulas into CTL formulas, interpreted over R TS . Then, the model checking algorithm for CTL =-=[3, 28]-=- applies. First, we have to extend R TS by a valuation function and make the definition of the set of atomic propositions a bit more precise. So, assume that AP is a finite set of propositions, which ... |

7 |
An axiomatization of event structures
- Mukund, Thiagarajan
- 1989
(Show Context)
Citation Context ..., conflict, and concurrency. The first temporal logic on prime event structures has been put forward by Lodaya and Thiagarajan [9]. Since then several new logics on event structures have been defined =-=[20, 21, 13, 14, 23]-=-. Most of these logics have been proved to be decidable and possessing complete axiomatizations. However, the model checking problem for event structure logics has never been addressed. The reason for... |

7 |
An axiomatization of well branching prime event structures, Report TCS-90-2
- Mukund, Thiagarajan
- 1990
(Show Context)
Citation Context ..., conflict, and concurrency. The first temporal logic on prime event structures has been put forward by Lodaya and Thiagarajan [9]. Since then several new logics on event structures have been defined =-=[20, 21, 13, 14, 23]-=-. Most of these logics have been proved to be decidable and possessing complete axiomatizations. However, the model checking problem for event structure logics has never been addressed. The reason for... |

7 |
A Temporal Logic for the Local Specification of Concurrent Systems
- Penczek
- 1989
(Show Context)
Citation Context |

4 |
editors. Time and logic: a computational approach
- Bolc, Szalas
- 1995
(Show Context)
Citation Context ... and therefore can be distinguished by DESL formulas corresponding to the causality relation. In the trace semantics of MUTEX (Figure 2) the traces: [ ]; [agbc]; [hdef ] lead to the same global state =-=(1; 2; 7)-=-, but the sets of global states to which lead their causal successors are different (see Figure 3). The solution is to sharpen the equivalence relation CTL accordingly. For technical reasons, the new ... |

3 |
Towards automata for branching time and partial order
- Huhn, P
- 1996
(Show Context)
Citation Context ... the state g n . Example 1. Program MUTEX is shown in Figure 1. It is composed of three processes, which local states are denoted with circles, whereas the transitions with horizontal bars, e.g. b = (=-=(3; 8)-=-; (5; 10)). The program ensures the mutual exclusion of access to the local states 5 and 6 being the critical sections. S 1 = f1; 3; 5g, S 2 = f2; 4; 6g, S 3 = f7; 8; 9; 10; 11g, and s 0 1 = 1, s 0 2 ... |

3 |
Trace Structures and other Models for Concurrency
- Nielsen, Winskel
- 1995
(Show Context)
Citation Context ...trace semantics of program MUTEX is shown in Figure 2. The prime traces are printed in bold face. 5.3 Event Structure Semantics of Programs Each trace system defines the corresponding event structure =-=[17]-=-, where the events are defined as equivalence classes of strings of transitions. For the trace systems that are semantics of the programs defined in Section 5.1, alternatively, one can identify the ev... |