11,564 research outputs found
Sliding Window Property Testing for Regular Languages
We study the problem of recognizing regular languages in a variant of the streaming model of computation, called the sliding window model. In this model, we are given a size of the sliding window n and a stream of symbols. At each time instant, we must decide whether the suffix of length n of the current stream ("the active window") belongs to a given regular language.
Recent works [Moses Ganardi et al., 2018; Moses Ganardi et al., 2016] showed that the space complexity of an optimal deterministic sliding window algorithm for this problem is either constant, logarithmic or linear in the window size n and provided natural language theoretic characterizations of the space complexity classes. Subsequently, [Moses Ganardi et al., 2018] extended this result to randomized algorithms to show that any such algorithm admits either constant, double logarithmic, logarithmic or linear space complexity.
In this work, we make an important step forward and combine the sliding window model with the property testing setting, which results in ultra-efficient algorithms for all regular languages. Informally, a sliding window property tester must accept the active window if it belongs to the language and reject it if it is far from the language. We show that for every regular language, there is a deterministic sliding window property tester that uses logarithmic space and a randomized sliding window property tester with two-sided error that uses constant space
Low-Latency Sliding Window Algorithms for Formal Languages
Low-latency sliding window algorithms for regular and context-free languages
are studied, where latency refers to the worst-case time spent for a single
window update or query. For every regular language it is shown that there
exists a constant-latency solution that supports adding and removing symbols
independently on both ends of the window (the so-called two-way variable-size
model). We prove that this result extends to all visibly pushdown languages.
For deterministic 1-counter languages we present a
latency sliding window algorithm for the two-way variable-size model where
refers to the window size. We complement these results with a conditional lower
bound: there exists a fixed real-time deterministic context-free language
such that, assuming the OMV (online matrix vector multiplication) conjecture,
there is no sliding window algorithm for with latency
for any , even in the most restricted sliding window model (one-way
fixed-size model). The above mentioned results all refer to the unit-cost RAM
model with logarithmic word size. For regular languages we also present a
refined picture using word sizes , ,
and .Comment: A short version will be presented at the conference FSTTCS 202
Property Testing of Regular Languages with Applications to Streaming Property Testing of Visibly Pushdown Languages
In this work, we revisit the problem of testing membership in regular languages, first studied by Alon et al. [Alon et al., 2001]. We develop a one-sided error property tester for regular languages under weighted edit distance that makes ?(?^{-1} log(1/?)) non-adaptive queries, assuming that the language is described by an automaton of constant size. Moreover, we show a matching lower bound, essentially closing the problem for the edit distance. As an application, we improve the space bound of the current best streaming property testing algorithm for visibly pushdown languages from ?(?^{-4} log? n) to ?(?^{-3} log? n log log n), where n is the size of the input. Finally, we provide a ?(max(?^{-1}, log n)) lower bound on the memory necessary to test visibly pushdown languages in the streaming model, significantly narrowing the gap between the known bounds
Low-Latency Sliding Window Algorithms for Formal Languages
Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language L it is shown that there exists a constant-latency solution that supports adding and removing symbols independently on both ends of the window (the so-called two-way variable-size model). We prove that this result extends to all visibly pushdown languages. For deterministic 1-counter languages we present a ?(log n) latency sliding window algorithm for the two-way variable-size model where n refers to the window size. We complement these results with a conditional lower bound: there exists a fixed real-time deterministic context-free language L such that, assuming the OMV (online matrix vector multiplication) conjecture, there is no sliding window algorithm for L with latency n^(1/2-?) for any ? > 0, even in the most restricted sliding window model (one-way fixed-size model). The above mentioned results all refer to the unit-cost RAM model with logarithmic word size. For regular languages we also present a refined picture using word sizes ?(1), ?(log log n), and ?(log n)
Apache Calcite: A Foundational Framework for Optimized Query Processing Over Heterogeneous Data Sources
Apache Calcite is a foundational software framework that provides query
processing, optimization, and query language support to many popular
open-source data processing systems such as Apache Hive, Apache Storm, Apache
Flink, Druid, and MapD. Calcite's architecture consists of a modular and
extensible query optimizer with hundreds of built-in optimization rules, a
query processor capable of processing a variety of query languages, an adapter
architecture designed for extensibility, and support for heterogeneous data
models and stores (relational, semi-structured, streaming, and geospatial).
This flexible, embeddable, and extensible architecture is what makes Calcite an
attractive choice for adoption in big-data frameworks. It is an active project
that continues to introduce support for the new types of data sources, query
languages, and approaches to query processing and optimization.Comment: SIGMOD'1
Visibly Pushdown Languages over Sliding Windows
We investigate the class of visibly pushdown languages in the sliding window model. A sliding window algorithm for a language L receives a stream of symbols and has to decide at each time step whether the suffix of length n belongs to L or not. The window size n is either a fixed number (in the fixed-size model) or can be controlled by an adversary in a limited way (in the variable-size model). The main result of this paper states that for every visibly pushdown language the space complexity in the variable-size sliding window model is either constant, logarithmic or linear in the window size. This extends previous results for regular languages
Subsequences in Bounded Ranges: Matching and Analysis Problems
In this paper, we consider a variant of the classical algorithmic problem of
checking whether a given word is a subsequence of another word . More
precisely, we consider the problem of deciding, given a number (defining a
range-bound) and two words and , whether there exists a factor
(or, in other words, a range of length ) of having as
subsequence (i.\,e., occurs as a subsequence in the bounded range
). We give matching upper and lower quadratic bounds for the time
complexity of this problem. Further, we consider a series of algorithmic
problems in this setting, in which, for given integers , and a word ,
we analyse the set -Subseq of all words of length which occur
as subsequence of some factor of length of . Among these, we consider
the -universality problem, the -equivalence problem, as well as problems
related to absent subsequences. Surprisingly, unlike the case of the classical
model of subsequences in words where such problems have efficient solutions in
general, we show that most of these problems become intractable in the new
setting when subsequences in bounded ranges are considered. Finally, we provide
an example of how some of our results can be applied to subsequence matching
problems for circular words.Comment: Extended version of a paper which will appear in the proceedings of
the 16th International Conference on Reachability Problems, RP 202
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