Streaming algorithms for recognizing nearly well-parenthesized expressions
Andreas Krebs, Nutan Limaye, Srikanth Srinivasan

TL;DR
This paper develops efficient streaming algorithms for recognizing nearly well-parenthesized expressions, specifically 1-turn-Dyck2 and Dyck2, with bounds on errors, space, and randomness, advancing understanding of approximate parenthesis matching in data streams.
Contribution
The paper introduces new randomized one-pass streaming algorithms for nearly well-parenthesized expressions with provable space and error bounds, and establishes lower bounds on space complexity.
Findings
Algorithms for 1-turn-Dyck2 with errors using O(k log n) space.
Algorithms for Dyck2 with errors using O(k log n + sqrt(n log n)) space.
Lower bounds showing Omega(k log(n/k)) space necessity for certain error thresholds.
Abstract
We study the streaming complexity of the membership problem of 1-turn-Dyck2 and Dyck2 when there are a few errors in the input string. 1-turn-Dyck2 with errors: We prove that there exists a randomized one-pass algorithm that given x checks whether there exists a string x' in 1-turn-Dyck2 such that x is obtained by flipping at most locations of x' using: - O(k log n) space, O(k log n) randomness, and poly(k log n) time per item and with error at most 1/poly(n). - O(k^{1+epsilon} + log n) space for every 0 <= epsilon <= 1, O(log n) randomness, O(polylog(n) + poly(k)) time per item, with error at most 1/8. Here, we also prove that any randomized one-pass algorithm that makes error at most k/n requires at least Omega(k log(n/k)) space to accept strings which are exactly k-away from strings in 1-turn-Dyck2 and to reject strings which are exactly (k+2)-away from strings in…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCryptography and Data Security · Complexity and Algorithms in Graphs · Algorithms and Data Compression
