Dynamic algorithms for the Dyck languages

Frandsen, Gudmund Skovbjerg; Husfeldt, Thore; Miltersen, Peter Bro; Rauhe, Theis; Skyum, Søren

doi:10.1007/3-540-60220-8_54

Cited by 8 publications

(17 citation statements)

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“…Let r −1 , r 0 , and r +1 denote the answer of query(2d + 2i) on y (g−1) , y (g) , and y (g+1) , respectively. By (11) in the proof of Proposition 3, if g = x 1 + · · · + x i , then r −1 r 0 r +1 = s d+i−1 s d+i s d+i+1 = 001. If instead g − 1 is the correct sum, then r −1 r 0 = 01, and finally if g + 1 is the correct sum, then r 0 r +1 = 00.…”

Section: Proof Of Theoremmentioning

confidence: 86%

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New Lower Bound Techniques for Dynamic Partial Sums and Related Problems

Husfeldt¹,

Rauhe²

2003

SIAM J. Comput.

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Abstract. We study the complexity of the dynamic partial sum problem in the cell-probe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer ±1 as an oracle and prove that the problem remains hard. This suggests which kind of information is hard to maintain.From these results, we derive a number of lower bounds for dynamic algorithms and data structures: We prove lower bounds for dynamic algorithms for existential range queries, reachability in directed graphs, planarity testing, planar point location, incremental parsing, and fundamental data structure problems like maintaining the majority of the prefixes of a string of bits. We prove a lower bound for reachability in grid graphs in terms of the graph's width. We characterize the complexity of maintaining the value of any symmetric function on the prefixes of a bit string.

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Section: Proof Of Theoremmentioning

confidence: 86%

“…We also present bounds for planar point location in monotone subdivisions [5,26], reachability in upward planar digraphs [28], and incremental parsing of balanced parentheses [11]. We show that these problems require time Ω(log n/ log log n) per operation .…”

mentioning

confidence: 99%

New Lower Bound Techniques for Dynamic Partial Sums and Related Problems

Husfeldt¹,

Rauhe²

2003

SIAM J. Comput.

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“…We first present the DynFO-program with polylogarithmic work for the membership problem of D 1 . It basically mimics the sequential algorithm from [8] that maintains D 1 sequentially in time O(log n), per change and query operation. Proof sketch.…”

Section: On Work-efficient Dynamic Programs For Dyck Languagesmentioning

confidence: 99%

“…In the algorithm of [8], the functions and r are updated in a bottom-up fashion. However, we will observe that they do not need to be updated sequentially in that fashion, but can be updated in parallel constant time.…”

Section: On Work-efficient Dynamic Programs For Dyck Languagesmentioning

confidence: 99%

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Work-sensitive Dynamic Complexity of Formal Languages

Schmidt

Schwentick

Tantau

et al. 2021

Lecture Notes in Computer Science

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Which amount of parallel resources is needed for updating a query result after changing an input? In this work we study the amount of work required for dynamically answering membership and range queries for formal languages in parallel constant time with polynomially many processors. As a prerequisite, we propose a framework for specifying dynamic, parallel, constant-time programs that require small amounts of work. This framework is based on the dynamic descriptive complexity framework by Patnaik and Immerman.

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