FACC: A Novel Finite Automaton Based on Cloud Computing for the Multiple Longest Common Subsequences Search

Table 1

Notations and their meanings.

Notations	Meaning
Σ	The common alphabet of N sequences
Σ𝑖	The set of alphabets in the ith sequence
𝑆𝑘(𝑘=1,2,…,𝑑)	The kth sequence, with d being the number of sequences drawn from Σ
T	A set of sequences drawn from Σ
𝑃=[𝑝1,𝑝2,…,𝑝𝑑]	A matched pair
𝑄={𝑄0,𝑄1,…,𝑄𝑛}	The set of the FA states
δ	The FA’s transition function
𝑄0=(0,0,…,0)	The FA’s initial state
F	The set of the FA’s final states
Atm	The FA recognizing/accepting all of the CSs of sequences from T
Σ^∗	Kleene closure of Σ, Σ^∗  ={𝑥∣𝑥 is a sequence from Σ with the length of zero or nonzero}
L(Atm)	A language recognized/accepted by the Atm