Enhanced regular expression language (ERE):

Atomic expressions:

   A    The empty traversal at class A
   lnk  a link of type lnk ("any" is a special case of any link type)

For combining expressions, the usual regular expression crowd:
   .     concatenation
   \cap  intersection
   \cup  union
   *     repetition
   not   negation

Note that A is like an empty string; the traversal that just sits at class
A.  As with all empty strings, A.A = A


Translation of series-parallel strategies to ERE
(enhanced regular expressions):

[A,B]			A.any*.B
through edges           any*.lnk.any*
bypassing edges         not(any*.lnk.any*)
through vertices        any*.A.any*
bypassing vertices      not(any*.A.any*)
d1 join d2              [d1].[d2]
d1 merge d2             [d1]\cup[d2]
d1 intersect d2         [d1]\cap[d2]
not d1                  not([d1])

where [x] is the translation of x into regular expressions.

Of course, \cap is not strictly necessary, as it can be expressed in terms
of \cup and not.  Furthermore, with distribution, not can be pushed down to
leaves.

Conjecture for Select-Sat for strategies:

[A,B]			polynomial	
through edges             "
bypassing edges           "
through vertices          "
bypassing vertices        "
d1 join d2         	polynomial
d1 merge d2       	polynomial
d1 intersect d2  	NP-complete
not d1          	NP-complete

Conjecture for Select-Sat for ERE:

   A    The empty traversal at class A
   lnk  a link of type lnk ("any" is a special case of any link type)
   .     concatenation		polynomial
   \cup  union		        polynomial
   *     repetition		polynomial
   \cap  intersection		NP-complete
   not   negation		NP-complete