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Definitions Edit

Given a symbol set \mathcal{L}, a sequence over \mathcal{L} is an ordered collection of symbols of \mathcal{L}, s=s_1s_2\cdots s_n,\ \forall i=1,\ldots,n\ s_i\in\mathcal{L}.

We call \mathcal{L}^* the set of all the sequences over \mathcal{L}.

Given s,t\in \mathcal{L}^*, we use the following notation:

  • \epsilon is the empty sequence.
  • s+t is the concatenation of s and t.
  • |s| is the length (number of symbols) of s.
  • s[i] is the i-th symbols of s.
  • s\sqsubseteq t represents that s is a subsequence of t, ie, there exist sequences u,v\in \mathcal{L}^* such that t=u+s+v.
  • s=t is the equality of sequences, ie., s\sqsubseteq t and t\sqsubseteq s.
  • s\#t is the number of times that the sequence s appears in the sequence t.

Similarity and distance functions Edit

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