Autocomplete PDO Exception with pgsql: syntax error at or near "REGEXP"

Problem

When running Drupal with PostgreSQL 9.1 and using the Advanced Link widget and set "start with specified characters" as auto complete suggestion type, after typing a character gives a PDO Exception like this:

PDOException: SQLSTATE[42601]: Syntax error: 7 ERROR: syntax error at or near "REGEXP" LINE 4: WHERE (mr.path REGEXP '^test[^\%]*$') ^: SELECT mr.path AS path FROM {menu_router} mr WHERE (mr.path REGEXP :db_condition_placeholder_0) LIMIT 10 OFFSET 0; Array ( [:db_condition_placeholder_0] => ^test[^\%]*$ ) in advanced_link_url_load() (line 87 of /var/www/xyz/public_html/sites/all/modules/contrib/advanced_link/advanced_link.module).

Problem: advanced_link.module uses REGEXP as sql condition, but pgsql doesn´t know about REGEXP.

An pgsql equivalent to mySQL REGEXP should be using POSIX Regular Expressions
http://www.postgresql.org/docs/9.1/static/functions-matching.html

So for pgsql it could be ~ instead of REGEXP:

    $result = db_select('menu_router', 'mr')
      ->fields('mr', array('path'))
      ->condition('mr.path', $condition_menu, '~')
      ->range(0, 10)->execute();

Proposed resolution

Maybe there should be a database connection type check before and then based on the result using the correct condition sql syntax.

How to get the current db connection type in Drupal 7?
Is there a function or variable?