## Automatic Abstraction in Symbolic Trajectory Evaluation

Citations: | 4 - 1 self |

### BibTeX

@MISC{Adams_automaticabstraction,

author = {Sara Adams and Magnus Björk and Tom Melham},

title = {Automatic Abstraction in Symbolic Trajectory Evaluation},

year = {}

}

### OpenURL

### Abstract

Abstract—Symbolic trajectory evaluation (STE) is a model checking technology based on symbolic simulation over a lattice of abstract state sets. The STE algorithm operates over families of these abstractions encoded by Boolean formulas, enabling verification with many different abstraction cases in a single modelchecking run. This provides a flexible way to achieve partitioned data abstraction. It is usually called ‘symbolic indexing ’ and is widely used in memory verification, but has seen relatively limited adoption elsewhere, primarily because users typically have to create the right indexed family of abstractions manually. This work provides the first known algorithm that automatically computes these partitioned abstractions given a reference-model specification. Our experimental results show that this approach not only simplifies memory verification, but also enables handling completely different designs fully automatically. I.

### Citations

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(Show Context)
Citation Context ... on automatic abstraction for model checking and verification. Some cornerstone techniques are localization reduction [10], counterexampleguided abstraction refinement [11], and predicate abstraction =-=[12]-=-. These and other methods have been extensively studied in the context of symbolic model-checking for hardware. By contrast, the literature on automatic abstraction for STE or GSTE is rather thin. One... |

597 | Counterexample-Guided Abstraction Refinement
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(Show Context)
Citation Context ...is a rich and growing literature on automatic abstraction for model checking and verification. Some cornerstone techniques are localization reduction [10], counterexampleguided abstraction refinement =-=[11]-=-, and predicate abstraction [12]. These and other methods have been extensively studied in the context of symbolic model-checking for hardware. By contrast, the literature on automatic abstraction for... |

101 |
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(Show Context)
Citation Context ... the specification to eliminate Xs, but in contrast with our work, does not in itself introduce complex, indexed families of abstractions. Finally, our algorithm bears a resemblance to the Dalgorithm =-=[15]-=- and other automatic test pattern generation methods. Both work backwards through a combinational circuit finding ways in which outputs might be forced high or low. VIII. CONCLUSION The algorithm we p... |

99 | Formal Verification by Symbolic Evaluation of Partially-Ordered Trajectories
- Seger, Bryant
- 1995
(Show Context)
Citation Context ...ompletely different designs fully automatically. I. INTRODUCTION Symbolic Trajectory Evaluation (STE) is a model checking technology based on symbolic simulation over a lattice of abstract state sets =-=[1]-=-. STE provides a combination of abstraction and algorithmic efficiency for verification of memories and datapath-dominated designs, and has tackled numerous difficult industrial verification problems ... |

76 |
Computer Aided Verification of Coordinating Processes
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(Show Context)
Citation Context ...r scheduler verification. VII. RELATED WORK There is a rich and growing literature on automatic abstraction for model checking and verification. Some cornerstone techniques are localization reduction =-=[10]-=-, counterexampleguided abstraction refinement [11], and predicate abstraction [12]. These and other methods have been extensively studied in the context of symbolic model-checking for hardware. By con... |

37 | A methodology for hardware verification based on logic simulation
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(Show Context)
Citation Context ...ery X by 0 or 1. The collection of all such abstractions forms a lattice, ordered by the amount of information about node values. The STE model-checking algorithm uses three-valued circuit simulation =-=[5]-=- to compute a reachable abstract state-set in this representation, comparing this to a specification written in a weak linear-time temporal logic. The algorithm is spaceefficient because it operates o... |

34 |
Introduction to generalized symbolic trajectory evaluation
- Yang, Seger
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(Show Context)
Citation Context ...sented in [13], slightly modified so it can handle indexing, is one promising option to consider. Finally, another obvious extension will be to incorporate the presented ideas into the GSTE algorithm =-=[16]-=-. We also intend to apply our method to a much wider class of problems to determine its strengths and weaknesses. We suspect this will yield more insight into how to further enhance our approach. ACKN... |

32 | An industrially effective environment for formal hardware verification
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(Show Context)
Citation Context ...nal targets for the use of symbolic indexing and one that illustrates the power of our algorithm in applying abstraction in more subtle ways. All results were obtained with BDD-based STE in the Forte =-=[3]-=- environment on a 2 Gbyte laptop. 0 1 n M key = = = Fig. 4. High-level model of CAM. Our first example is a traditional content-addressable memory (CAM), as illustrated in Fig. 4. The verification we ... |

23 |
Level Formal Verification of Next-Generation Microprocessors
- Schubert, “High
- 2003
(Show Context)
Citation Context ...E provides a combination of abstraction and algorithmic efficiency for verification of memories and datapath-dominated designs, and has tackled numerous difficult industrial verification problems [2]–=-=[4]-=-. In the abstraction lattice at the heart of STE, each circuit node is assigned a value in the set {0,1,X}, with ‘X’ representing an unknown or ‘don’t care’ value. An assignment of such values to ever... |

21 | The Mathematical Foundation of Symbolic Trajectory Evaluation
- Chou
- 1999
(Show Context)
Citation Context ...sult verified in this abstract model transfers over to the real, Boolean model of circuit states. Formally, there is a Galois connection between the three-valued model and the Boolean model of states =-=[6]-=-. On top of the abstraction lattice, STE provides a layer of symbolic representation whereby whole families of abstractions may be checked simultaneously in one run of the modelCarl-Johan Seger Strate... |

20 | Formal verification of content addressable memories using symbolic trajectory evaluation
- Pandey, Raimi, et al.
- 1997
(Show Context)
Citation Context .... STE provides a combination of abstraction and algorithmic efficiency for verification of memories and datapath-dominated designs, and has tackled numerous difficult industrial verification problems =-=[2]-=-–[4]. In the abstraction lattice at the heart of STE, each circuit node is assigned a value in the set {0,1,X}, with ‘X’ representing an unknown or ‘don’t care’ value. An assignment of such values to ... |

9 | Abstraction by Symbolic Indexing Transformations
- Melham, Jones
- 2002
(Show Context)
Citation Context ...f abstractions from the specification to be verified. The abstraction scheme is then encoded in the guards of the verification property using the indexing transformation algorithm of Melham and Jones =-=[7]-=-. The result is an automatic abstraction method for STE, which requires little or no user guidance. We illustrate the effectiveness of our method with verifications of a memory, a CAM, and a simple sc... |

9 | SAT-based Assistance in Abstraction Refinement for Symbolic Trajectory Evaluation
- Roorda, Claessen
- 2006
(Show Context)
Citation Context .... A heuristic algorithm is presented in [13] that assigns fresh, distinct Boolean variables to input nodes in a clever way targeted at eliminating the Xs that make the model-checking run fail. Roorda =-=[14]-=- presents a SAT-based method that assists in manual abstraction refinement for STE. The algorithm provides the user with hints for refining abstractions that over-approximate circuit behaviour. For a ... |

8 | Automatic refinement and vacuity detection for symbolic trajectory evaluation
- Tzoref, Grumberg
- 2006
(Show Context)
Citation Context ...d in the context of symbolic model-checking for hardware. By contrast, the literature on automatic abstraction for STE or GSTE is rather thin. One notable exception is the work of Tzoref and Grumberg =-=[13]-=- on abstraction refinement for STE. This addresses the problem of over-abstraction in STE that manifests itself in symbolic simulation by a node carrying X where thesconsequent expects 0 or 1. This is... |

3 |
Non-linear Quantification Scheduling
- Chauhan, Clarke, et al.
(Show Context)
Citation Context ... partitioned abstraction relation, which allows early existential quantification to be used in the preimage computations explained in Section II-A. We can, for example, use the technique described in =-=[9]-=-. But we can do even better by exploiting the special form that our relations have by virtue of how they are generated. First, it is easy to show that the abstraction relation R[X, T ] generated by ou... |