Testing Membership in Parenthesis Languages

Michal Parnas*, Dana Ron, Ronitt Rubinfeld

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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(n2/33), where ε is the given distance parameter. Furthermore, we improve the lower bound for testing Dyck languages to Ω̃(n1/11) for constant ε. We also describe a testing algorithm for the context free language LREV = {uurvvr: u, v ∈ ∑*}, where 2 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].

Original languageEnglish
Pages (from-to)98-138
Number of pages41
JournalRandom Structures and Algorithms
Issue number1
StatePublished - Jan 2003


Dive into the research topics of 'Testing Membership in Parenthesis Languages'. Together they form a unique fingerprint.

Cite this