Automatic Abstraction without Counterexamples

McMillan, Kenneth L.; Amla, Nina

doi:10.1007/3-540-36577-x_2

Cited by 144 publications

(130 citation statements)

References 20 publications

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“…Another perspective on the obtained counterexample is to consider them as a logical combination of multiple counterexamples. Refining multiple counterexamples simultaneously has been shown empirically to perform well in practice [16], which is also confirmed by our experimental evaluation.…”

Section: Examplesupporting

confidence: 83%

“…In some cases, it might happen that while refining a shorter, thinner and local counterexample the breadth-first strategy might get lucky and the new predicates discovered may prune a large state space in the next iteration. But in general both from our experience from the experiments and as presented in [16], refining more counterexamples simultaneously provides a higher chance of discovering better predicates and faster fixpoint arrival.…”

Section: Methodsmentioning

confidence: 93%

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Subsumer-First: Steering Symbolic Reachability Analysis

Rybalchenko

Singh

2009

Model Checking Software

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Abstract. Symbolic reachability analysis provides a basis for the verification of software systems by offering algorithmic support for the exploration of the program state space when searching for proofs or counterexamples. The choice of exploration strategy employed by the analysis has direct impact on its success, whereas the ability to find short counterexamples quickly and-as a complementary task-to efficiently perform the exhaustive state space traversal are of utmost importance for the majority of verification efforts. Existing exploration strategies can optimize only one of these objectives which leads to a sub-optimal reachability analysis, e.g., breadth-first search may sacrifice the exploration efficiency and chaotic iteration can miss minimal counterexamples. In this paper we present subsumer-first, a new approach for steering symbolic reachability analysis that targets both minimal counterexample discovery and efficiency of exhaustive exploration. Our approach leverages the result of fixpoint checks performed during symbolic reachability analysis to bias the exploration strategy towards its objectives, and does not require any additional computation. We demonstrate how the subsumer-first approach can be applied to improve efficiency of software verification tools based on predicate abstraction. Our experimental evaluation indicates the practical usefulness of the approach: we observe significant efficiency improvements (median value 40%) on difficult verification benchmarks from the transportation domain.

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Section: Examplesupporting

confidence: 83%

Section: Methodsmentioning

confidence: 93%

Subsumer-First: Steering Symbolic Reachability Analysis

Rybalchenko

Singh

2009

Model Checking Software

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“…If v was originally not flagged then it may happen that one of its new parents v l and v r may not contain the literals corresponding to piv(v) (line 9-12). In this case, v is treated as a flagged node(line [13][14]. Please look in [3] for more detailed description of RestoreResTree.…”

Section: Conjunctive Normal Form(cnf)mentioning

confidence: 99%

“…Unsatisfiability proofs for a Boolean formula can find many applications in verification. For instance, one application is automatic learning of abstractions for unbounded model checking by analyzing proofs of program safety for bounded steps [14,13,10]. We can also learn unsatisfiable cores from unsatisfiability proofs, which are useful in locating errors in inconsistent specifications [22].…”

Section: Introductionmentioning

confidence: 99%

Improved Single Pass Algorithms for Resolution Proof Reduction

Gupta

2012

Theory and Applications of Satisfiability Testing – SAT 2012

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Abstract. Unsatisfiability proofs find many applications in verification. Today, many SAT solvers are capable of producing resolution proofs of unsatisfiability. For efficiency smaller proofs are preferred over bigger ones. The solvers apply proof reduction methods to remove redundant parts of the proofs while and after generating the proofs. One method of reducing resolution proofs is redundant resolution reduction, i.e., removing repeated pivots in the paths of resolution proofs (aka Pivot recycle). The known single pass algorithm only tries to remove redundancies in the parts of the proof that are trees. In this paper, we present three modifications to improve the algorithm such that the redundancies can be found in the parts of the proofs that are DAGs. The first modified algorithm covers greater number of redundancies as compared to the known algorithm without incurring any additional cost. The second modified algorithm covers even greater number of the redundancies but it may have longer run times. Our third modified algorithm is parametrized and can trade off between run times and the coverage of the redundancies. We have implemented our algorithms in OpenSMT and applied them on unsatisfiability proofs of 198 examples from plain MUS track of SAT11 competition. The first and second algorithm additionally remove 0.89% and 10.57% of clauses respectively as compared to the original algorithm. For certain value of the parameter, the third algorithm removes almost as many clauses as the second algorithm but is significantly faster.

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“…In abstraction refinement of model checking [2,3,4,5], the abstract model grows larger after refinement, which potentially prohibits the success of model checking for an enormous state space. The abstraction for next iteration is constructed by identification of an unsatisfiable core to rule out its spurious counterexamples.…”

Section: Introductionmentioning

confidence: 99%

Variable Minimal Unsatisfiability

Chen

Ding

2006

Lecture Notes in Computer Science

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Abstract. In this paper, we present variable minimal unsatisfiability (VMU), which is a generalization of minimal unsatisfiability (MU). A characterization of a VMU formula F is that every variable of F is used in every resolution refutation of F . We show that the class of VMU formulas is D P -complete. For fixed deficiency (the difference of the number of clauses and the number of variables), the VMU formulas can be solved in polynomial time. Furthermore, we investigate more subclasses of VMU formulas. Although the theoretic results on VMU and MU are similar, some observations are shown that the extraction of VMU may be more practical than MU in some cases.

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Automatic Abstraction without Counterexamples

Cited by 144 publications

References 20 publications

Subsumer-First: Steering Symbolic Reachability Analysis

Subsumer-First: Steering Symbolic Reachability Analysis

Improved Single Pass Algorithms for Resolution Proof Reduction

Variable Minimal Unsatisfiability

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