Dynamic Algorithms for the Dyck Languages

Abstract

Abstract. We study dynamic membership problems for the Dyck languages, the class of strings of properly balanced parentheses. We also study the Dynamic Word problem for the free group. We present deterministic algorithms and data structures which maintain a string under replacements of symbols, insertions, and deletions of symbols, and language membership queries. Updates and queries are handled in polylogarithmic time. We also give both Las Vegas-and Monte Carlo-type randomised algorithms to achieve better running times, and present lower bounds on the complexity for variants of the problems.

The dynamic complexity of formal languages

“…Here, the focus is not on structural (parallel) complexity of updates but rather on (sequential) update time [17,18]. In particular, [9,10] give efficient incremental algorithms and analyse the complexity of formal language classes based on completely different ideas.…”

“…Here, the focus is not on structural (parallel) complexity of updates but rather on (sequential) update time [17,18]. In particular, [9,10] give efficient incremental algorithms and analyse the complexity of formal language classes based on completely different ideas. Another area related to dynamic formal languages is the incremental maintenance of schema information (aka regular tree languages) [1,2] and XPath query evaluation [3] in XML documents.…”