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Abstract
This chapter discusses the interface between formal language theory and computational complexity theory. The results concerning the description of languages, whether by grammars, automata, or other means, belong to the first area, that is, formal language theory and possibly to the second area, that is, the complexity theory. The results concerning the number of steps, the amount of memory, or the size of an algorithm required for a given task belong to the second area and possibly the first. The problems in computational complexity are described as language recognition problems and traditional formal language theory classes are described as complexity classes. The separation results indicate how much additional computing resource is needed to obtain a larger family of languages. The recursive padding technique leads to stronger separation results in the case of space-bounded Turing machines, space-bounded auxiliary pushdown automata, and nondeterministic time-bounded Turing machines. The chapter describes the method by considering nondeterministic time-bounded Turing machines.
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