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**Computing invariants with transformers: experimental scalability and accuracy.**
*(English)*
Zbl 1337.68168

Simon, Axel (ed.) et al., Proceedings of the 5th international workshop on numerical and symbolic abstract domains, NSAD 2014, Munich, Germany, September 10, 2014. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 307, 17-31, electronic only (2014).

Summary: Using abstract interpretation, invariants are usually obtained by solving iteratively a system of equations linking preconditions according to program statements. However, it is also possible to abstract first the statements as transformers, and then propagate the preconditions using the transformers. The second approach is modular because procedures and loops can be abstracted once and for all, avoiding an iterative resolution over the call graph and all the control flow graphs.

However, the transformer approach based on polyhedral abstract domains encurs two penalties: some invariant accuracy may be lost when computing transformers, and the execution time may increase exponentially because the dimension of a transformer is twice the dimension of a precondition.

The purposes of this article are 1) to measure the benefits of the modular approach and its drawbacks in terms of execution time and accuracy using significant examples and a newly developed benchmark for loop invariant analysis, ALICe, 2) to present a new technique designed to reduce the accuracy loss when computing transformers, 3) to evaluate experimentally the accuracy gains this new technique and other previously discussed ones provide with ALICe test cases and 4) to compare the executions times and accuracies of different tools, ASPIC, ISL, PAGAI and PIPS.

Our results suggest that the transformer-based approach used in PIPS, once improved with transformer lists, is as accurate as the other tools when dealing with the ALICe benchmark. Its modularity nevertheless leads to shorter execution times when dealing with nested loops and procedure calls found in real applications.

For the entire collection see [Zbl 1310.68020].

However, the transformer approach based on polyhedral abstract domains encurs two penalties: some invariant accuracy may be lost when computing transformers, and the execution time may increase exponentially because the dimension of a transformer is twice the dimension of a precondition.

The purposes of this article are 1) to measure the benefits of the modular approach and its drawbacks in terms of execution time and accuracy using significant examples and a newly developed benchmark for loop invariant analysis, ALICe, 2) to present a new technique designed to reduce the accuracy loss when computing transformers, 3) to evaluate experimentally the accuracy gains this new technique and other previously discussed ones provide with ALICe test cases and 4) to compare the executions times and accuracies of different tools, ASPIC, ISL, PAGAI and PIPS.

Our results suggest that the transformer-based approach used in PIPS, once improved with transformer lists, is as accurate as the other tools when dealing with the ALICe benchmark. Its modularity nevertheless leads to shorter execution times when dealing with nested loops and procedure calls found in real applications.

For the entire collection see [Zbl 1310.68020].

### MSC:

68Q60 | Specification and verification (program logics, model checking, etc.) |

68N30 | Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) |

### Keywords:

model checking; abstract interpretation; static program analysis; linear relation analysis; automatic invariant detection; loop invariant; transformer; benchmark
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\textit{V. Maisonneuve} et al., Electron. Notes Theor. Comput. Sci. 307, 17--31 (2014; Zbl 1337.68168)

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