2004-02-18: There is an unfortunate mistake on p. 202 of the book in Table 3.31: Precedence of Opeators from
High to Low. According to this table, the high-precedence
crossproduct operator : outranks
everything else, followed by the prefix operators such as ~ (complement) \ (term complement), and $ (contains)
that are said to outrank suffix operators such as *
(Kleene plus) and + (Kleene
star) and other iteration operators. This is true only for the term
complement operator \ but
false for the other prefix operators, as illustrated by the examples
equivalent to [\a]*
not equivalent to \[a*]
equivalent to ~[a*]
not equivalent to
In the original book release of xfst
(version 8.1.7), expressions such
as \a:b are
not accepted as valid. Because the high precedence crossproduct
operator outranks the term complement, \a:b is
equivalent to the illegal expression \[a:b].
Note that term complement operator can only be used to modify a regular
language and is not applicable to a regular relations sucah as the pair a:b.
is equivalent to
$[a^2] not equivalent to
$a+ is equivalent to
$[a+] not equivalent to
Starting with the 8.3.9 release of xfst, the term complement operator
outranks the colon. Consequently, an expression such as \a:b is
now legal and equivalent to [\a]:b designating
the relation that maps any single character symbol other than a to b.
The correct operator precedence table for version 8.3.9 and later xfst
versions is given below. It includes the substitution operator `
(see page 51 in the book) that was inadvertently left out of the
original table and the precede < and follow operators that appear in
the precedence table but are not discussed anywhere in the book.
The correct precedence table for xfst-8.1.7
on the book CD can be derived from the above table by exchanging the
first two lines.
+ * ^ .1 .2 .u .l .i .r
Kleene plus and star, iteration, upper-lower, invert and reverse
~ $ $. $?
Complement, symbol complement,
Concatenation (no overt operator)
Precede and follow
| & -
=> -> (->) @->
etc. Rule operators
Crossproduct and compose
Precedence of Operators from High to Low.
Last Modified:Wednesday, 18-Feb-2004 18:23:38 PST