## Sat-based compositional verification using lazy learning (2007)

Venue: | In CAV |

Citations: | 10 - 1 self |

### BibTeX

@INPROCEEDINGS{Sinha07sat-basedcompositional,

author = {Nishant Sinha and Edmund Clarke},

title = {Sat-based compositional verification using lazy learning},

booktitle = {In CAV},

year = {2007},

pages = {3--5}

}

### OpenURL

### Abstract

be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. Keywords: Assume-Guarantee Reasoning, SAT, SMT, BMC, Learning A recent approach to automated assume-guarantee reasoning (AGR) for concurrent systems relies on computing environment assumptions for components using the L ∗ algorithm for learning regular languages. While this approach has been investigated extensively for message passing systems, it still remains a challenge to scale the technique to large shared memory systems, mainly because the assumptions have an exponential communication alphabet size. In this paper, we propose a SAT-based methodology that employs both induction and interpolation to implement automated AGR for shared memory systems. The method is based on a new lazy approach to assumption learning, which avoids an explicit enumeration of the exponential alphabet set during learning by using symbolic alphabet clustering and iterative counterexample-driven localized partitioning. Preliminary experimental results on benchmarks in Verilog and SMV are encouraging and show that the approach scales well in practice. 1

### Citations

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Citation Context ...(their languages are regular), then a finite state assumption A exists. Therefore, the task of computing A is cast as a machine learning problem, where an algorithm for learning regular languages L ∗ =-=[5, 33]-=- is used to automatically compute A. The L ∗ learner computes a deterministic finite automaton (DFA) corresponding to an unknown regular language by asking queries to a teacher entity, which is capabl... |

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Citation Context ...scharge them on its environment (i.e., the other components). The primary bottleneck is that these approaches require us to manually provide appropriate environment assumptions. Recently, an approach =-=[15]-=- has been proposed to automatically generate these assumptions using learning algorithms for regular languages assisted by a model checker. Figure 1 shows a simplified view of this approach for an AGR... |

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Citation Context ...rform more efficient counterexample analysis by differentiating positive and negative counterexamples (cf. Section 4). In contrast to the counterexample-guided abstraction refinement (CEGAR) approach =-=[23, 14, 7]-=-, the assumption languages may change non-monotonically across iterations of the learning algorithm. The CEGAR approach removes spurious behaviors from an abstraction by adding new predicates. In cont... |

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Citation Context ...rform more efficient counterexample analysis by differentiating positive and negative counterexamples (cf. Section 4). In contrast to the counterexample-guided abstraction refinement (CEGAR) approach =-=[23, 14, 7]-=-, the assumption languages may change non-monotonically across iterations of the learning algorithm. The CEGAR approach removes spurious behaviors from an abstraction by adding new predicates. In cont... |

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Citation Context ...e found in [19, 27, 13]. SAT-based bounded model checking for LTL properties was proposed by Biere et al. [10] and several improvements, including techniques for making it complete have been proposed =-=[30, 4]-=-. All the previous approaches are non-compositional, i.e., they build a monolithic transition relation for the whole system. To the best of our knowledge, our work in the first to address automated co... |

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Citation Context ...them back iteratively. A learning algorithm for parameterized systems (alphabet consists of a small set of basis symbols, each of which is parameterized by a set of boolean variables) was proposed in =-=[9]-=-. Our lazy learning algorithm is different: we reason about a set of traces directly using a SAT-based model checker and perform more efficient counterexample analysis by differentiating positive and ... |

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5 |
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Citation Context ...n STSs M1, M2 and CFA P , show that M1 � M2 � P , by picking an assumption CFA A, such that both (n1) M1 � A � P and (n2) M2 � A hold. The following circular rule has also been proposed in literature =-=[8, 27]-=-. Definition 3 Circular AGR (C) Show that M1 � M2 � P holds by picking an CFA assumption tuple, 〈A1,A2〉, such that each of the following hold: (c1) M1 � A1 � P (c2) M2 � A1 � P and (c3) A1 � A2 � P . ... |

4 |
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Citation Context ...artitioning, the BDD-based approach may introduce unnecessary states in the assumptions. Recently, two approaches for improved learning based on alphabet under-approximation and iterative enlargement =-=[12, 19]-=- have been proposed. Our lazy approach is complementary: while the above techniques try to reduce the overall alphabet by under-approximation, our technique tries to compactly represent a large alphab... |

4 |
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Citation Context ...ic algorithms in [31, 27]. The problem of whether it is possible to obtain good decompositions of systems for this approach has been studied in [16]. An overview of other related work can be found in =-=[19, 27, 13]-=-. SAT-based bounded model checking for LTL properties was proposed by Biere et al. [10] and several improvements, including techniques for making it complete have been proposed [30, 4]. All the previo... |

3 |
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