On the relative complexity of some languages in NC
Information Processing Letters
Pseudorandom generators for space-bounded computations
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
On the power of quantum fingerprinting
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The communication complexity of the Hamming distance problem
Information Processing Letters
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Communication Complexity
Data Stream Algorithms via Expander Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Weak Derandomization of Weak Algorithms: Explicit Versions of Yao's Lemma
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Recognizing well-parenthesized expressions in the streaming model
Proceedings of the forty-second ACM symposium on Theory of computing
Data stream algorithms for codeword testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Optimal bounds for Johnson-Lindenstrauss transforms and streaming problems with sub-constant error
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Streaming algorithms for some problems in log-space
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
| Hi-index | 0.00 |
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′ ∈ 1-turn-Dyck2 such that x is obtained by flipping at most k 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/nΩ(1). - O(k1+ε + log n) space for every 0 ≤ ε ≤ 1, O(log n) randomness, O((logO(1) n + kO(1))) 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 Ω(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 1-turn-Dyck2. Since 1-turn-Dyck2 and the Hamming Distance problem are closely related we also obtain new upper and lower bounds for this problem. Dyck2 with errors: We prove that there exists a randomized one-pass algorithm that given x checks whether there exists a string x′ ∈ Dyck2 such that x is obtained from x′ by changing (in some restricted manner) at most k positions using: - O(k log n + √n log n) space, O(k log n) randomness, poly(k log n) time per element and with error at most 1/nΩ(1). - O(k1+ε + √n log n) space for every 0 O(log n) randomness, O((logO(1) n + kO(1))) time per element, with error at most 1/8.