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The Decidability and Complexity of Interleaved Bidirected Dyck Reachability
[article]
2021
arXiv
pre-print
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As many static analyses yield a certain type of bidirected graphs, they give rise to interleaved bidirected Dyck reachability problems. ...
Interleaved Dyck reachability (denoted D_k⊙ D_k) uses two Dyck languages for increased precision (e.g., context and field sensitivity) but is well-known to be undecidable. ...
We also thank anonymous reviewers for their constructive feedback. ...
arXiv:2111.05923v1
fatcat:4j6is3jfbna3xc5axxek4nptwi
On the complexity of bidirected interleaved Dyck-reachability
2021
Proceedings of the ACM on Programming Languages (PACMPL)
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that uses a fast algorithm to over-approximate language-reachability on a directed graph. ...
Interleaved Dyck-reachability (InterDyck-reachability), denoted by 𝐷 𝑘 ⊙ 𝐷 𝑘 -reachability, is a natural extension of Dyck-reachability that allows one to formulate program-analysis problems that involve ...
ACKNOWLEDGEMENTS We would like to thank the anonymous POPL reviewers for valuable feedback on earlier drafts of this paper, which helped improve its presentation. ...
doi:10.1145/3434340
fatcat:7ucdwclbuvhjvgzqoid46ooyzu
Indexing Context-Sensitive Reachability
[article]
2021
arXiv
pre-print
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This paper presents Flare, a reduction from the CFL reachability problem to the conventional graph reachability problem for context-sensitive data flow analysis. ...
Many context-sensitive data flow analyses can be formulated as a variant of the all-pairs Dyck-CFL reachability problem, which, in general, is of sub-cubic time complexity and quadratic space complexity ...
ACKNOWLEDGEMENTS We would like to thank the anonymous reviewers and Peisen Yao for their valuable feedback on our earlier paper draft. ...
arXiv:2109.01321v1
fatcat:hdkh7nzfvrgihjapg4l6utnwyq
The Fine-Grained and Parallel Complexity of Andersen's Pointer Analysis
[article]
2020
arXiv
pre-print
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First, we establish an O(n^3) upper-bound for general APA, improving over O(n^2· m) as n=O(m). Second, we show that even on-demand APA ("may a specific pointer a point to a specific location b?") ...
Bradford for bringing to our attention his result on D 1 -Reachability and for helpful comments in comparing his algorithm to ours, as well as anonymous reviewers for their constructive feedback in an ...
Dyck Reachability and Representation of Andersen's Pointer Analysis Here we develop some notation on Dyck languages and Dyck reachability, and use it to represent instances of APA as Dyck graphs. ...
arXiv:2006.01491v3
fatcat:7egcvj77jvcy5migd47cnquy7a
The fine-grained and parallel complexity of andersen's pointer analysis
2021
Proceedings of the ACM on Programming Languages (PACMPL)
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First, we establish an 𝑂 (𝑛 3 ) upper-bound for general APA, improving over 𝑂 (𝑛 2 • 𝑚) as 𝑛 = 𝑂 (𝑚). ...
CCS Concepts: • Software and its engineering → Software verification and validation; • Theory of computation → Theory and algorithms for application domains; Program analysis. ...
Bradford for bringing to our attention his result on D 1 -Reachability and for helpful comments in comparing his algorithm to ours, as well as anonymous reviewers for their constructive feedback in an ...
doi:10.1145/3434315
fatcat:qtuyvgtwibcqzbfzgihyxxh4x4
Correct and Efficient Accelerator Programming (Dagstuhl Seminar 13142)
2013
unpublished
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This is a survey of algorithms for approximating a curve by a simpler curve, mostly by a polygon with few edges. ...
In the last part I also mention an algorithm of Drysdale, Rote, and Sturm [1] for smooth (tangent-continuous) approximation by biarcs. ...
drawings[1]: Brinkman graph, Dyck graph, and F40 (dodecahedron double cover). ...
fatcat:m7452gw4cvecbd2vi6w3uha5ai