α := 
β := 

   ~α = ϕ
   ~β = ϕ
α < β = false
α = β = true
α > β = false
α & β = .*
α ^ β = ϕ
α - β = ϕ

s := 

s ∈ α = true
s ∈ β = true

|α| = 0
|β| = 0

dfa(α) has 0 states

dfa(β) has 0 states


regex syntax

  .         match any single character
  xy        concatenation: match x and then y
  x|y       alternation: match x or y
  x*        kleene star: match x zero-or-more times
  (xyz)     grouping: treat xyz as a single item (e.g. (xyz)*)
  ()        an empty regex matches the empty string
  x+        kleene plus: match x one-or-more times (equivalent to xx*)
  x?        optional: optionally match x (equivalent to (x|))
  x{n}      exponentiatio