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
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
Regular Languages are Testable with a Constant Number of Queries
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Testing of function that have small width branching programs
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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
omega-Regular Languages Are Testable with a Constant Number of Queries
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Streaming algorithms for recognizing nearly well-parenthesized expressions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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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/Ɛ3), where Ɛ is the given distance parameter. Furthermore, we improve the lower bound for testing Dyck languages to Ω(n1/11) for constant Ɛ. We also have a testing algorithm for the context free language LREV = {w = uurvvr: w ∈ Σn}, where Σ is a fixed alphabet. The running time of our algorithm is Õ(√n/Ɛ), which almost matches the lower bound given by Alon et al. [1].