CHAPTER 3 - Formal Languages and Power Series

Abstract

This chapter discusses formal language theory and focuses on a specific tool called formal power series. Formal language theory, together with automata theory, is the oldest branch of theoretical computer science. The chapter discusses the fundamental notions about formal power series and languages. It also various normal forms for grammars. The chapter describes a class of generating devices that are somewhat different from grammars but still equivalent to grammars in the sense that the family of languages generated by the new devices equals the family of recursively enumerable languages. The new devices, called Post canonical systems or Post systems, very closely resemble formal systems in logic. The productions have the shape of inference rules. The family of languages generated by Post systems equals the family of recursively enumerable languages. The chapter discusses Markov algorithms, which resemble the intuitive notion of an algorithm. Viewed as language-defining devices, Markov algorithms are equivalent to grammars and Post systems.