Scanning list structures without stacks or tag bits

Lindstrom, Gary

doi:10.1016/0020-0190(73)90012-4

Cited by 30 publications

(27 citation statements)

References 3 publications

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“…For all the above classes of algorithms, for those cases in which triple order traversal is loop-free but preorder, inorder and postorder traversal are not, the technique employed by Lindstrom [11] and described above will enable us to obtain loop-free algorithms for single-visit "random" order traversal. A similar technique can be used if, for example, preinorder traversal is loop-free but preorder and inorder traversal are not.…”

Section: Classification Of Algorithms~mentioning

confidence: 98%

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Loop-free algorithms for traversing binary trees

Fenner

Loizou

1984

BIT

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Abstract.We survey and classify the various algorithms for traversing binary trees in the three principal orders and the related two-and three-visit traversal orders. For each class of algorithms we determine which of the traversal orders may be effected by means of loop-free traversal algorithms.Although, in general, these are multi-visit traversal orders, we indicate how the algorithms may be modified to yield loop-free sinole-visit traversal algorithms in "non-standard" orders. We also exhibit and discuss the close relationship between the various stack-based algorithms and the other classes of algorithms.

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Section: Classification Of Algorithms~mentioning

confidence: 98%

“…(This is easy to prove by induction on the number of nodes in the tree.) The required algorithm (Lindstrom [11], Algorithm 5) is thus obtained by only including every third node visit, i.e. those with the same visit number mod 3.…”

Section: Classification Of Algorithms~mentioning

confidence: 99%

Loop-free algorithms for traversing binary trees

Fenner

Loizou

1984

BIT

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“…As an example of possible application, we have analyzed (by hand) the Deutsch-Schorr-Waite data structure traversal algorithm [SW67]. In fact, we consider the version of [Lin73], dedicated to data structures without cycles, and which does not involve any auxiliary marking. A slightly different version of this algorithm has been completely proven with TVLA [LRS06].…”

Section: An Example With Linked Data Structuresmentioning

confidence: 99%

An Analysis of Permutations in Arrays

Perrelle¹,

Halbwachs²

2010

Lecture Notes in Computer Science

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Abstract. This paper is concerned with the synthesis of invariants in programs with arrays. More specifically, we consider properties concerning array contents up to a permutation. For instance, to prove a sorting procedure, one has to show that the result is sorted, but also that it is a permutation of the initial array. In order to analyze this kind of properties, we define an abstract interpretation working on multisets of values, and able to discover invariant equations about such multisets.

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“…Verification of the above property using the powerset heap abstraction took 584 cpu seconds and generated 189, 772 different shape descriptorsdefinitely too many for such a simple program and simple property. The situation is worse for verifying a similar property for an implementation of the Deutsch-Schorr- Waite scanning procedure [11]. This verification took 4 hours when the powerset heap abstraction was used.…”

Section: Running Examplementioning

confidence: 99%

Partially Disjunctive Heap Abstraction

Manevich

Sagiv

Ramalingam³

et al. 2004

Static Analysis

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Abstract.One of the continuing challenges in abstract interpretation is the creation of abstractions that yield analyses that are both tractable and precise enough to prove interesting properties about real-world programs. One source of difficulty is the need to handle programs with different behaviors along different execution paths. Disjunctive (powerset) abstractions capture such distinctions in a natural way. However, in general, powerset abstractions increase space and time costs by an exponential factor. Thus, powerset abstractions are generally perceived as very costly. In this paper, we partially address this challenge by presenting and empirically evaluating a new heap abstraction. The new heap abstraction works by merging shape descriptors according to a partial isomorphism similarity criteria, resulting in a partially disjunctive abstraction. We implemented this abstraction in TVLA-a generic system for implementing program analyses.We conducted an empirical evaluation of the new abstraction and compared it with the powerset heap abstraction. The experiments show that analyses based on the partially disjunctive heap abstraction are as precise as the ones based on the powerset heap abstraction. In terms of performance, analyses based on the partially disjunctive heap abstraction are often superior to analyses based on the powerset heap abstraction. The empirical results show considerable speedups, up to 2 orders of magnitude, enabling previously non-terminating analyses, such as verification of the Deutsch-Schorr-Waite scanning algorithm, to terminate with no negative effect on the overall precision. Indeed, experience indicates that the partially disjunctive shape abstraction improves performance across all TVLA analyses uniformly, and in many cases is essential for making precise shape analysis feasible.

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Scanning list structures without stacks or tag bits

Cited by 30 publications

References 3 publications

Loop-free algorithms for traversing binary trees

Loop-free algorithms for traversing binary trees

An Analysis of Permutations in Arrays

Partially Disjunctive Heap Abstraction

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