Introduction to Computational Linguistics

12. Finite State Automata 37
Suppose that the first character is at position 1230. Then the string 129.023
matches the first bracket and the string 145.110 the second bracket. These strings
can be recalled using the function matched_group. It takes as input a number
and the original string, and it returns the string of the nth matching bracket. So, if
directly after the match on the string assigned to u we define
(104)
let s = "The first half of the IP address is
"^(Str.matched_group 1 u)
we get the following value for s:
(105) "The first half of the IP address is 129.23
To use this in an automated string replacement procedure, the variables \\0, \\1,
\\2,..., \\9. After a successful match, \\0 is assigned to the entire string, \\1, to
the first matched string, \\2 to the second matched string, and so on. A template
is a string that in place of characters also contains these variables (but nothing
more). The function global_replace takes as input a regular expression, and
two strings. The first string is used as a template. Whenever a match is found it
uses the template to execute the replacement. For example, to cut the IP to its first
half, we write the template "\\1". If we want to replace the original IP address
by its first part followed by .0.1, then we use "\\.0.1". If we want to replace the
second part by the first, we use "\\1.\\".
12 Finite State Automata
A finite state automaton is a quintuple
(106) A = 〈A, Q, i 0 , F, δ〉
where A, the alphabet, is a finite set, Q, the set of states, also is a finite set,
i 0 ∈ Q is the initial state, F ⊆ Q is the set of final or accepting states and,
finally, δ ⊆ Q × A × Q is the transition relation. We write x → a y if 〈x, a, y〉 ∈ δ.