Sender Restrictions to Aliases/Address in Postfix

From the Postfix documentation, it appears you need to modify this section in your main.cf file:

http://www.postfix.org/ADDRESS_VERIFICATION_README.html

/etc/postfix/main.cf:
    smtpd_sender_restrictions = 
        permit_mynetworks
        ... 
        check_sender_access hash:/etc/postfix/sender_access
        reject_unknown_sender_domain
        warn_if_reject reject_unverified_sender 
        ...
    # Postfix 2.6 and later.
    # unverified_sender_reject_reason = Address verification failed

    # Default setting for Postfix 2.7 and later.
    # Note 1: Be sure to read the "Caching" section below!
    # Note 2: Avoid hash files here. Use btree instead.
    address_verify_map = btree:/var/lib/postfix/verify

This will put warning messages in your logs when a sender fails verification, but it won't reject it. You can remove the warn_if_reject line if you don't want to pollute your log files.

UPDATE:

If you want regular expressions, you'll need to compile PCRE support into Postfix (if it's not there already):

http://www.postfix.org/PCRE_README.html

Then, you can simply replace the line check_sender_access hash:/etc/postfix/sender_access with: check_sender_access pcre:/etc/postfix/sender_access and it will check for regex's in that file. If you're using Debian/Ubuntu, there's a package called postfix-pcre that will install support for PCRE.

http://www.postfix.org/pcre_table.5.html

Adding alpha.example.com to /etc/postfix/mydomains fixed the problem.

On a LAN with dozens or hundreds of servers this would be annoying to maintain, perhaps there's a more general solution?