1.The usual set operations,such as union,intersection,difference,and complement with respect to E*.
2.Concatenation: Let La,Lb⊆E*，then
LaLb:={s∈E*:(s=sasb)and(sa⊆La)and(sb∈Lb)}
3.Prefix-closure: Let L⊆E*,then
L(L的逆):={s∈E*:(∃t∈E*)[st∈L]}
4.Kleene-closure: Let L⊆E*,then
L*:={ε}∪L∪LL∪LLL∪· · ·
5.Post-language: Let L⊆E* and s∈L.then the post-language of L after s,denoted by L/s,is the language
L/s:={t∈E*:st∈L}
6.An automaton is a device that is capable of representing a language according to welldefined rules.
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