Conventional computers suffer from several communication bottlenecks which fundamentally limit their performance. These bottlenecks are characterized by an address-dependent sequential transfer of information which arises from the need to time-multiplex information over a limited number of interconnections. An optical digital computer based on a classical finite state machine can be shown to be free of these bottlenecks. Such a processor would be unique since it would be capable of modifying its entire state space each cycle while conventional computers can only alter a few bits. New algorithms are needed to manage and use this capability. A technique based on recognizing a particular symbol in parallel and replacing it in parallel with another symbol is suggested. Examples using this parallel symbolic substitution to perform binary addition and binary incrementation are presented. Applications involving Boolean logic, functional programming languages, production rule driven artificial intelligence, and molecular chemistry are also discussed.