Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Automata and Computability
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
Testing the diameter of graphs
Random Structures & Algorithms
Testing properties of directed graphs: acyclicity and connectivity
Random Structures & Algorithms
Testing of function that have small width branching programs
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Space Complexity Vs. Query Complexity
Computational Complexity
Hierarchy Theorems for Property Testing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Recognizing well-parenthesized expressions in the streaming model
Proceedings of the forty-second ACM symposium on Theory of computing
Hierarchy theorems for property testing
Property testing
Hierarchy theorems for property testing
Property testing
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We continue the investigation of properties defined by formal languages. This study was initiated by Alon et al. [1], who described an algorithm for testing properties defined by regular languages. Alon et al. also considered several context free languages, and in particular Dyck languages, which contain strings of properly balanced parentheses. They showed that the first Dyck language, which contains strings over a single type of pairs of parentheses, is testable in time independent of n, where n is the length of the input string. However, the second Dyck language, defined over two types of parentheses, requires Ω (log n) queries. Here we describe a sublinear-time algorithm for testing all Dyck languages. Specifically, the running time of our algorithm is Õ(n2/3/ε3), where ε is the given distance parameter. Furthermore, we improve the lower bound for testing Dyck languages to Ω (n1/11) for constant ε. We also describe a testing algorithm for the context free language LREV = {uurvvr : u, v ∈ Σ*}, where Σ is a fixed alphabet. The running time of our algorithm is Õ(√n/ε), which almost matches the lower bound given by Alon et al. [1].