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The Decidability and Complexity of Interleaved Bidirected Dyck Reachability [article]

Adam Husted Kjelstrøm, Andreas Pavlogiannis
2021 arXiv   pre-print
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

Yuanbo Li, Qirun Zhang, Thomas Reps
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
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]

Qingkai Shi, Yongchao Wang, Charles Zhang
2021 arXiv   pre-print
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]

Anders Alnor Mathiasen, Andreas Pavlogiannis
2020 arXiv   pre-print
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

Anders Alnor Mathiasen, Andreas Pavlogiannis
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
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)

Bernadette Charron-Bost, Stepahn Merz, Andrey Rybalchenko, Josef Widder, Albert Cohen, Alastair Donaldson, Marieke Huisman, Joost-Pieter Katoen, Stephen Kobourov, Martin Nöllenburg, Monique, Sergiu Hart (+2 others)
2013 unpublished
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