Abstract
This chapter discusses the behavior of finite outputless automata. The chapter reviews several concepts that are useful in formulating criteria for a language to be finite-state. It describes various operations under which the class of finite-state languages is closed. The concepts of distinguishability and interchangeability enable to characterize the memory capacity required to represent a given language (ω-language). The chapter discusses the concepts of probabilistic automaton and grammar with an eye to the concepts of language representation that they define. The chapter focuses on the operations under which the class of finite-state languages is closed. This class is closed under many operations. The operations fall into two groups: (1) set-theoretic and logical, and (2) operations defined in terms of word concatenation. In all cases, proofs of closure properties yield effective closure, that is, they prove the existence of an algorithm which, given anchored (macro-anchored) finite automata, construct the resultant anchored (macro-anchored) automaton.
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