I want to use this to find out whether the other application I'm talking to via a socket has crashed.

You can use the tcp keepalive feature of tcp/ip.

You must setup a reasonable period of check ( the default is too high ).
Inside your application you check for the incoming data using the function select().
When the line on the other end is dropped you will receive an input from the select, but the message read is empty.
to setup the tcp_keepalive_time you must
LINUX change the value in /proc/sys/net/ipv4/tcp_keepalive_time

# echo 60 > /proc/sys/net/ipv4/tcp_keepalive_time

WINDOWS modify a value in the registry
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Tcpip\Parameters "KeepAliveTime"=dword:0000ea61

You should also enable the keepalive and linger option using the setsockopt function. I give you an example in C. The function setsockopt is also available in perl.

         int ierr;
         bool optval = true;
         ierr = setsockopt( Socket->SocketHandle,
                                 SOL_SOCKET,
                                 SO_KEEPALIVE,
                                 (const char FAR * ) &optval,
                                 sizeof(bool));
         if( ierr == 0 )
         {
             linger struct_linger;
             struct_linger.l_onoff  = 1;
             struct_linger.l_linger = 0;
             ierr = setsockopt( Socket->SocketHandle,
                                     SOL_SOCKET,
                                     SO_LINGER,
                                     (const char FAR * ) &struct_linger,
                                     sizeof(linger));

I hope this info should help
regards, Enzo