What causes a system to satisfy a specification?

Chockler, Hana; Halpern, Joseph Y.; Kupferman, Orna

doi:10.1145/1352582.1352588

Cited by 62 publications

(65 citation statements)

References 37 publications

(66 reference statements)

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“…However, each of the marksmen has degree of blame 1/10. The complexity of determining the degree of responsibility and blame using the original definition of causality was completely characterized (Chockler & Halpern, 2004;Chockler, Halpern, & Kupferman, 2008). Again, we show that changing the definition of causality affects the complexity, and completely characterize the complexity of determining the degree of responsibility and blame with the updated definition.…”

Section: Introductionmentioning

confidence: 76%

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The Computational Complexity of Structure-Based Causality

Aleksandrowicz

Chockler

Halpern

et al. 2017

jair

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Halpern and Pearl introduced a definition of actual causality; Eiter and Lukasiewicz showed that computing whether X = x is a cause of Y = y is NP-complete in binary models (where all variables can take on only two values) and Σ P 2 -complete in general models. In the final version of their paper, Halpern and Pearl slightly modified the definition of actual cause, in order to deal with problems pointed out by Hopkins and Pearl. As we show, this modification has a nontrivial impact on the complexity of computing whether X = x is a cause of Y = y. To characterize the complexity, a new family D P k , k = 1, 2, 3, . . ., of complexity classes is introduced, which generalizes the class D P introduced by Papadimitriou and Yannakakis (D P is just D P 1 ).We show that the complexity of computing causality under the updated definition is D P 2 -complete. Chockler and Halpern extended the definition of causality by introducing notions of responsibility and blame, and characterized the complexity of determining the degree of responsibility and blame using the original definition of causality. Here, we completely characterize the complexity using the updated definition of causality. In contrast to the results on causality, we show that moving to the updated definition does not result in a difference in the complexity of computing responsibility and blame.

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Section: Introductionmentioning

confidence: 76%

“…In the original HP model, it was shown that computing responsibility is FP NP[log n] -complete in binary causal models (Chockler et al, 2008) and FP Σ P 2 [log n] -complete in general causal models (Chockler & Halpern, 2004). First, we prove that the FP Σ P 2 [log n] -completeness result holds for singleton causes.…”

Section: Responsibilitymentioning

confidence: 93%

The Computational Complexity of Structure-Based Causality

Aleksandrowicz

Chockler

Halpern

et al. 2017

jair

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“…We obtain tractability by restricting our queries to conjunctive queries. Chockler et al [6] have shown that causality for "read once" Boolean circuits is in PTIME. Our results are strictly stronger: for the case of conjunctive queries without self-joins, queries with read-once lineage expressions are precisely the hierarchical queries [8,20], while our results apply to all conjunctive queries.…”

Section: Complexity Of Causalitymentioning

confidence: 99%

The complexity of causality and responsibility for query answers and non-answers

et al. 2010

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An answer to a query has a well-defined lineage expression (alternatively called how-provenance) that explains how the answer was derived. Recent work has also shown how to compute the lineage of a non-answer to a query. However, the cause of an answer or non-answer is a more subtle notion and consists, in general, of only a fragment of the lineage. In this paper, we adapt Halpern, Pearl, and Chockler's recent definitions of causality and responsibility to define the causes of answers and non-answers to queries, and their degree of responsibility. Responsibility captures the notion of degree of causality and serves to rank potentially many causes by their relative contributions to the effect. Then, we study the complexity of computing causes and responsibilities for conjunctive queries. It is known that computing causes is NP-complete in general. Our first main result shows that all causes to conjunctive queries can be computed by a relational query which may involve negation. Thus, causality can be computed in PTIME, and very efficiently so. Next, we study computing responsibility. Here, we prove that the complexity depends on the conjunctive query and demonstrate a dichotomy between PTIME and NP-complete cases. For the PTIME cases, we give a non-trivial algorithm, consisting of a reduction to the max-flow computation problem. Finally, we prove that, even when it is in PTIME, responsibility is complete for LOGSPACE, implying that, unlike causality, it cannot be computed by a relational query.

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“…In order to achieve an efficiently computable approximation, our algorithm is inspired by the algorithm for read-once formulas in [3]. It involves one traversal of the circuit for each l ∈ I X (r) and its overall complexity is only quadratic in the size of M .…”

Section: Computing Degree Of Responsibility In Treesmentioning

confidence: 99%

“…Inspired by the algorithm for read-once formulas in [3], we developed the algorithm RespST E for efficiently computing an approximate DoR. Computing the responsibility of the inputs for some output of a circuit involves one traversal of the circuit for each X valued input in the cone of influence of the output.…”

Section: Introductionmentioning

confidence: 99%

Efficient Automatic STE Refinement Using Responsibility

Chockler

Grumberg

Yadgar

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Symbolic Trajectory Evaluation (STE) is a powerful technique for hardware model checking. It is based on 3-valued symbolic simulation, using 0,1, and X ("unknown"). X is used to abstract away values of circuit nodes, thus reducing memory and runtime of STE runs. The abstraction is derived from a given user specification.An STE run results in "pass" (1), if the circuit satisfies the specification, "fail" (0) if the circuit falsifies it, and "unknown" (X), if the abstraction is too coarse to determine either of the two. In the latter case, refinement is needed: The X values of some of the abstracted inputs should be replaced. The main difficulty is to choose an appropriate subset of these inputs that will help to eliminate the "unknown" STE result, while avoiding an unnecessary increase in memory and runtime. The common approach to this problem is to manually choose these inputs.This work suggests a novel approach to automatic refinement for STE, which is based on the notion of responsibility. For each input with X value we compute its Degree of Responsibility (DoR) to the "unknown" STE result. We then refine those inputs whose DoR is maximal.We implemented an efficient algorithm, which is linear in the size of the circuit, for computing the approximate DoR of inputs. We used it for refinements for STE on several circuits and specifications. Our experimental results show that DoR is a very useful device for choosing inputs for refinement. In comparison with previous works on automatic refinement, our computation of the refinement set is faster, STE needs fewer refinement iterations and uses less overall memory and time.

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What causes a system to satisfy a specification?

Cited by 62 publications

References 37 publications

The Computational Complexity of Structure-Based Causality

The Computational Complexity of Structure-Based Causality

The complexity of causality and responsibility for query answers and non-answers

Efficient Automatic STE Refinement Using Responsibility

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