Descriptional Complexity of Machines with Limited Resources

Over the last 30 years or so many results have appeared on the descriptional complexity of machines with limited resources. Since these results have appeared in a variety of different contexts, our goal here is to provide a survey of these results. Particular emphasis is put on limiting resources (e.g., nondeterminism, ambiguity, lookahead, etc.) for various types of finite state machines, pushdown automata, parsers and cellular automata and on the effect it has on their descriptional complexity. We also address the question of how descriptional complexity might help in the future to solve practical issues, such as software reliability.