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DFA Minimization Algorithms in Map-Reduce


DFA Minimization Algorithms in Map-Reduce

Hedayati Somarin, Iraj (2016) DFA Minimization Algorithms in Map-Reduce. Masters thesis, Concordia University.

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Map-Reduce has been a highly popular parallel-distributed programming model. In this thesis, we study the problem of minimizing Deterministic Finite State Automata (DFA). We focus our attention on two well-known (serial) algorithms, namely the algorithms of Moore (1956) and of Hopcroft (1971). The central cost-parameter in Map-Reduce is that of communication cost i.e., the amount of data that has to be communicated between the processes. Using techniques from Communication Complexity we derive an O(kn log{n}) lower bound and O(kn^3 log{n}) upper bound for the problem, where n is the number of states in the DFA to be minimized,and k is the size of its alphabet. We then develop Map-Reduce versions of both Moore's and Hopcroft's algorithms, and show that their communication cost is O(kn^2 (log {n} + log {k})). Both methods have been implemented and tested on large DFA, with 131,072 states. The experiments verify our theoretical analysis, and also reveal that Hopcroft's algorithm -- considered superior in the sequential framework -- is very sensitive to skew in the topology of the graph of the DFA, whereas Moore's algorithm handles skew without major efficiency loss.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering
Item Type:Thesis (Masters)
Authors:Hedayati Somarin, Iraj
Institution:Concordia University
Degree Name:M. Comp. Sc.
Program:Computer Science
Date:17 January 2016
Thesis Supervisor(s):Grahne, Gösta K.
Keywords:Map-Reduce, Big-Data, Hadoop, Automata, DFA Minimization, Communication Complexity, Parallel, Distributed, Complexity Model
ID Code:980838
Deposited On:16 Jun 2016 14:40
Last Modified:18 Jan 2018 17:52


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