### Abstract

When a system fails to satisfy its specification, the model checker produces an error trace (or counter-example) that demonstrates an undesirable behavior, which is then used in debugging the system. Error explanation is the task of discovering errors in the system or the reasons why the system exhibits the error trace. While there has been considerable recent interest in automating this task and developing tools based on different heuristics, there has been very little effort in characterizing the computational complexity of the problem of error explanation. In this paper, we study the complexity of two popular heuristics used in error explanation. The first approach tries to compute the smallest number of system changes that need to be made in order to ensure that the given counter-example is no longer exhibited, with the intuition being that these changes are the errors that need fixing. The second approach relies on the observation that differences between correct and faulty runs of a system shed considerable light on the sources of errors. In this approach, one tries to compute the correct trace of the system that is closest to the counter-example. We consider three commonly used abstractions to model programs and systems, namely, finite state Mealy machines, extended finite state machines and pushdown automata. We show that the first approach of trying to find the fewest program changes is NP-complete no matter which of the three formal models is used to represent the system. Moreover we show that no polynomial factor approximation algorithm for computing the smallest set of changes is possible, unless P = NP. For the second approach, we present a polynomial time algorithm that finds the closest correct trace, when the program is represented by a Mealy machine or a pushdown automata. When the program is represented by an extended finite state machine, the problem is once again NP-complete, and no polynomial factor approximation algorithm is likely.

Original language | English (US) |
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Pages (from-to) | 448-464 |

Number of pages | 17 |

Journal | Lecture Notes in Computer Science |

Volume | 3385 |

State | Published - Sep 9 2005 |

Event | 6th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2005 - Paris, France Duration: Jan 17 2005 → Jan 19 2005 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science*,

*3385*, 448-464.