457 research outputs found
Subsequence Automata with Default Transitions
Let be a string of length with characters from an alphabet of size
. The \emph{subsequence automaton} of (often called the
\emph{directed acyclic subsequence graph}) is the minimal deterministic finite
automaton accepting all subsequences of . A straightforward construction
shows that the size (number of states and transitions) of the subsequence
automaton is and that this bound is asymptotically optimal.
In this paper, we consider subsequence automata with \emph{default
transitions}, that is, special transitions to be taken only if none of the
regular transitions match the current character, and which do not consume the
current character. We show that with default transitions, much smaller
subsequence automata are possible, and provide a full trade-off between the
size of the automaton and the \emph{delay}, i.e., the maximum number of
consecutive default transitions followed before consuming a character.
Specifically, given any integer parameter , , we
present a subsequence automaton with default transitions of size
and delay . Hence, with we
obtain an automaton of size and delay . On
the other extreme, with , we obtain an automaton of size and delay , thus matching the bound for the standard subsequence
automaton construction. Finally, we generalize the result to multiple strings.
The key component of our result is a novel hierarchical automata construction
of independent interest.Comment: Corrected typo
Finding Frequent Subsequences in a Set of Texts
Given a set of strings, the Common Subsequence Automaton accepts all common subsequences of these strings. Such an automaton can be deduced from other automata like the Directed Acyclic Subsequence Graph or the Subsequence Automaton. In this paper, we introduce some new issues in text algorithm on the basis of Common Subsequences related problems. Firstly, we make an overview of different existing automata, focusing on their similarities and differences. Secondly, we present a new automaton, the Constrained Subsequence Automaton, which extends the Common Subsequence Automaton, by adding an integer denoted quorum
Negative Factor: Improving Regular-Expression Matching in Strings
Conference paper version 2013, SIGMOD '13 Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data, http://dx.doi.org/10.1145/2463676.2465289</p
Negative Factor: Improving Regular-Expression Matching in Strings
Conference paper version 2013, SIGMOD '13 Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data, http://dx.doi.org/10.1145/2463676.2465289</p
Regular Specifications of Resource Requirements for Embedded Control Software
For embedded control systems, a schedule for the allocation of resources to a software component can be described by an infinite word whose ith symbol models the resources used at the ith sampling interval. Dependency of performance on schedules can be formally modeled by an automaton (w-regular language) which captures all the schedules that keep the system within performance requirements. We show how such an automaton is constructed for linear control designs and exponential stability or settling time performance requirements. Then, we explore the use of the automaton for online scheduling and for schedulability analysis. As a case study, we examine how this approach can be applied for the LQG control design. We demonstrate, by examples, that online schedulers can be used to guarantee performance in worst-case condition together with good performance in normal conditions. We also provide examples of schedulability analysis
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