The files listed in Project Properties > Publish > Application Files
is automatically compiled by Visual Studio. Your application must require these DLLs. If they are not already registered on the machine then setting them to excluded
will generate the error you describe.
You should either set the assemblies to Included
or if this adds unacceptable size overhead to your distribution then you can go to Project Properties > Publish > Prerequisites
and add SQL Server 2012 Express LocalDB