Regarding your update...

The query is a simple /yyy

There is no {}yyy element at the root (or anywhere else in your XML document), so LibXML is correct in returning nothing.

You want to match the {http://xxx}yyy element, so you need to use

my $parser = XML::LibXML->new();
my $doc    = $parser->parse_file($file_name);
my $root   = $doc->documentElement();

my $xpc = XML::LibXML::XPathContext->new();
$xpc->registerNs( xxx => 'http://xxx' );

for my $node ( $xpc->findnodes('/xxx:xxx/xxx:yyy', $root) ) {
   ...
}
[download]

As I mentioned earlier, this is documented in XML::LibXML::Node, under findnodes, under "NOTE ON NAMESPACES AND XPATH".

"xxx" can be replaced with any identifier you wish, as long as you use what you pass to registerNS in your queries.

Update: I had forgotten the include the root node in the XPath. Fixed.