Abstract
This chapter provides an overview of finite automata (FA). The chapter focuses on using automata and formal languages in the context of the specification or design of a software component, which is called the component under design. An alphabet, typically represented with the Greek letter ∑, is a finite set of symbols called letters. In practice, these symbols are the names of events or conditions in the domain of discourse for the component under design. A requirement is a specification of legal scenarios for a component under design. Regular expressions (REs) are a substitute for set notation used to specify requirements as sets of scenarios. With REs, the standard set-notation braces are stripped off, and the set union operator is written as a “+”.FA have a textual definition and a graphical counterpart called finite state diagrams. A multitape FA is an FA in which the domain of discourse alphabet is the composition, or Cartesian product, of several “smaller,” independent alphabets. Fully and partially specified deterministic finite automata (DFA), a nondeterministic FA (NFA), universal FA, and alternating FA (AFA) are also discussed in the chapter.
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