## A Technique of State Space Search Based on Unfolding (1992)

Venue: | Formal Methods in System Design |

Citations: | 66 - 0 self |

### BibTeX

@INPROCEEDINGS{Mcmillan92atechnique,

author = {K. L. Mcmillan and D. K. Probst},

title = {A Technique of State Space Search Based on Unfolding},

booktitle = {Formal Methods in System Design},

year = {1992},

pages = {45--65}

}

### Years of Citing Articles

### OpenURL

### Abstract

Unfoldings of Petri nets provide a method of searching the state space of concurrent systems without considering all possible interleavings of concurrent events. A procedure is given for constructing the unfolding of a Petri net, terminating the construction when it is sufficient to represent all reachable markings. This procedure is applied to hazard and deadlock detection in asynchronous circuits. Examples are given of scalable systems with exponential size state spaces, but polynomial size unfoldings, including a distributed mutual exclusion ring circuit.

### Citations

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Symbolic Model Checking: 10 States and Beyond
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- 1992
(Show Context)
Citation Context ...ts a method which requires quadratic space and time in the number of cells, though it requires a pomtree model of the circuit to be constructed by hand. Finally, the symbolic model checking technique =-=[2]-=- has also been applied to the DME circuit. The basic symbolic model checking algorithm requires cubic time and linear space (in the number of cells). Burch and Long 7 have obtained O(n 2:5 ) time for ... |

258 |
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Citation Context ... [13] circuit designed to implement a distributed mutual exclusion (DME) protocol. The circuit was designed by Alain Martin [8] and has been analyzed using an abstracted trace theoretic model by Dill =-=[4]-=-. Networks of logic gates in speed-independent circuits are readily modeled by Petri nets. A network of n gates can be modeled by a Petri net of O(n) places. When we model a network of gates as a Petr... |

204 |
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Citation Context ...nd deadlock. However, it is plausible that unfoldings could be used for various verification problems that involve state space search, such as conformation checking [4], temporal logic model checking =-=[3]-=-, or language containment of !-automata [7]. Conformation checking seems to be the most natural candidate, since it deals only with finite sequences. In such a program, trace structures might be model... |

176 |
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Citation Context ... Probst and Li [10], [11], [12], and has been used in the verification of asynchronous circuits. 2 Another framework for a partially ordered analysis has been provided by Nielsen, Plotkin and Winskel =-=[9]-=-. They describe the unfolding of a model called a Petri net into an infinite net of a restricted form called an occurrence net. From the occurrence net, one can derive a partial order (one might say a... |

166 | Symbolic model checking with partitioned transition relations
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Citation Context ... checking algorithm requires cubic time and linear space (in the number of cells). Burch and Long 7 have obtained O(n 2:5 ) time for the DME using symbolic model checking with a modified search order =-=[1]-=-. This method requires some hand optimization, however. In any event, it appears that the symbolic model checking method yields somewhat better asymptotic performance for the DME circuit, though both ... |

163 | Stubborn sets for reduced state space generation.Advances
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Citation Context ...noring the (irrelevant) 2 K. L. MCMILLAN ordering of moves leads to a much simpler (in fact trivial) analysis. Might such be the case with concurrent systems? This question has been approached before =-=[14]-=-, [15], [5], [6], [16]. Valmari and Godefroid have (independently) observed that the notion of persistence is an important one in determining when move ordering can be ignored. A persistent move is on... |

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Using Partial Orders to Improve Automatic Verification Methods
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Citation Context ...irrelevant) 2 K. L. MCMILLAN ordering of moves leads to a much simpler (in fact trivial) analysis. Might such be the case with concurrent systems? This question has been approached before [14], [15], =-=[5]-=-, [6], [16]. Valmari and Godefroid have (independently) observed that the notion of persistence is an important one in determining when move ordering can be ignored. A persistent move is one which rem... |

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Citation Context ...evant) 2 K. L. MCMILLAN ordering of moves leads to a much simpler (in fact trivial) analysis. Might such be the case with concurrent systems? This question has been approached before [14], [15], [5], =-=[6]-=-, [16]. Valmari and Godefroid have (independently) observed that the notion of persistence is an important one in determining when move ordering can be ignored. A persistent move is one which remains ... |

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Citation Context ...the net. Coverability of this latter place is equivalent to coverability of the set. 4. Application example We now consider a more realistic example than the dining philosophers -- a speedindependent =-=[13]-=- circuit designed to implement a distributed mutual exclusion (DME) protocol. The circuit was designed by Alain Martin [8] and has been analyzed using an abstracted trace theoretic model by Dill [4]. ... |

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Citation Context ... a more realistic example than the dining philosophers -- a speedindependent [13] circuit designed to implement a distributed mutual exclusion (DME) protocol. The circuit was designed by Alain Martin =-=[8]-=- and has been analyzed using an abstracted trace theoretic model by Dill [4]. Networks of logic gates in speed-independent circuits are readily modeled by Petri nets. A network of n gates can be model... |

13 |
A stubborn attack on the state explosion problem
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Citation Context ... the (irrelevant) 2 K. L. MCMILLAN ordering of moves leads to a much simpler (in fact trivial) analysis. Might such be the case with concurrent systems? This question has been approached before [14], =-=[15]-=-, [5], [6], [16]. Valmari and Godefroid have (independently) observed that the notion of persistence is an important one in determining when move ordering can be ignored. A persistent move is one whic... |

10 |
Testing containment of !-regular languages
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Citation Context ...unfoldings could be used for various verification problems that involve state space search, such as conformation checking [4], temporal logic model checking [3], or language containment of !-automata =-=[7]-=-. Conformation checking seems to be the most natural candidate, since it deals only with finite sequences. In such a program, trace structures might be modeled with Petri nets. Verification of trace c... |

7 |
Using partial order semantics to avoid the state explosion problem in asynchronous systems
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Citation Context ...n moves or transitions, and choice, or bifurcation in A TECHNIQUE OF STATE SPACE SEARCH BASED ON UNFOLDING 3 the search. One such structure, called a pomtree, has been invented by Probst and Li [10], =-=[11]-=-, [12], and has been used in the verification of asynchronous circuits. 2 Another framework for a partially ordered analysis has been provided by Nielsen, Plotkin and Winskel [9]. They describe the un... |

5 |
Acceleration of timing verification method based on time Petri nets
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Citation Context ...) 2 K. L. MCMILLAN ordering of moves leads to a much simpler (in fact trivial) analysis. Might such be the case with concurrent systems? This question has been approached before [14], [15], [5], [6], =-=[16]-=-. Valmari and Godefroid have (independently) observed that the notion of persistence is an important one in determining when move ordering can be ignored. A persistent move is one which remains possib... |

2 |
Partial order model checking: A guide for the perplexed
- Probst, Li
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(Show Context)
Citation Context ...s or transitions, and choice, or bifurcation in A TECHNIQUE OF STATE SPACE SEARCH BASED ON UNFOLDING 3 the search. One such structure, called a pomtree, has been invented by Probst and Li [10], [11], =-=[12]-=-, and has been used in the verification of asynchronous circuits. 2 Another framework for a partially ordered analysis has been provided by Nielsen, Plotkin and Winskel [9]. They describe the unfoldin... |

1 |
Abstract specification, composition, and proof of correctness of delay-insensitive circuits and systems
- Probst, Li
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(Show Context)
Citation Context ...rder on moves or transitions, and choice, or bifurcation in A TECHNIQUE OF STATE SPACE SEARCH BASED ON UNFOLDING 3 the search. One such structure, called a pomtree, has been invented by Probst and Li =-=[10]-=-, [11], [12], and has been used in the verification of asynchronous circuits. 2 Another framework for a partially ordered analysis has been provided by Nielsen, Plotkin and Winskel [9]. They describe ... |