## Section: New Results

### Assume-Guarantee reasoning

#### Simultaneous Assume-Guarantee reasoning through learning

Participants : Fei He, Bow-Yaw Wang, He Zhu.

To generate finite automata as contextual assumptions, the exact
learning algorithm L^{*} for finite automata is used. In the simplest
setting, the system under verification is decomposed into two
components. An instance of the L^{*} algorithm is deployed to find a
proper contextual assumption to verify the system. In more realistic
settings, the optimal decomposition may consist of several components
[54] . One could deploy several independent instances
of the L^{*} algorithm to find assumptions for these components. The
naïve deployment however would disregard semantic information among
components. In this project, we would like to incorporate such
information into instances of the L^{*} algorithm. We have discussed
ideas to coordinate the construction of contextual assumptions in each
L^{*} algorithm.

#### Implicit Assume-Guarantee reasoning through learning

Participant : Bow-Yaw Wang.

Contextual assumptions are required to apply assume-guarantee reasoning. Previously, assumptions are computed explicitly [36] . It has been reported that the explicit assume-guarantee reasoning is less efficient than explicit monolithic algorithms. To address this problem, we apply an exact learning algorithm for Boolean formulae to generate assumptions implicitly. For the invariant checking problem, our new algorithm derives initial predicates and transition relations represented by Boolean formulae implicitly. We have implemented a prototype. Preliminary experiments show that our algorithm is comparable to monolithic SAT-based algorithms for small cases.

#### Data mining based decomposition for Assume-Guarantee reasoning

Participants : Ming Gu, Fei He, He Zhu.

Automated compositional reasoning using assume-guarantee rules plays a key role in large system verification. A vexing problem is to discover fine decomposition of system contributing to appropriate assumptions. In [16] , we present with William N. N. Hung and Xiaoyu Song an automatic decomposition approach in compositional reasoning verification. The method is based on data mining algorithms. An association rule algorithm is harnessed to discover the hidden rules among system variables. A hypergraph partitioning algorithm is proposed to incorporate these rules as weight constraints for system variable clustering. The experiments demonstrate that our strategy leads to order-of-magnitude speedup over previous.