The Space Complexity of Recognizing Well-Parenthesized Expressions in the Streaming Model: The Index Function Revisited

  title={The Space Complexity of Recognizing Well-Parenthesized Expressions in the Streaming Model: The Index Function Revisited},
  author={R. Jain and Ashwin Nayak},
  journal={IEEE Transactions on Information Theory},
  • R. Jain, Ashwin Nayak
  • Published 2014
  • Mathematics, Computer Science, Physics
  • IEEE Transactions on Information Theory
  • We show an Ω(√n/T) lower bound for the space required by any unidirectional constant-error randomized T-pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well parenthesized. This proves a conjecture due to Magniez, Mathieu, and Nayak (2009) and rigorously establishes that bidirectional streams are exponentially more efficient in space usage as compared with unidirectional ones. We obtain the lower bound by analyzing the information that is… CONTINUE READING
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