The Chomsky Hierarchy: Four Computers

The Chomsky Hierarchy: Four Computers Aimee Blackburn Chapter 7

Outline of my Glorious Presentation • (Brief!) History of Chomsky’s linguistic theories • Overview of the Hierarchy itself • How does this information pertain to the realm of computer science?

Who is Noam Chomsky Anyway? • Philosopher of Languages • Professor of Linguistics at MIT • Constructed the idea that language was not a learned “behavior”, but that it was cognitive and innate; versus stimulus-response driven • In an effort to explain these theories, he developed the Chomsky Hierarchy

Chomsky Hierarchy • Comprises four types of languages and their associated grammars and machines. • Type 3: Regular Languages • Type 2: Context-Free Languages • Type 1: Context-Sensitive Languages • Type 0: Recursively Enumerable Languages • These languages form a strict hierarchy

Chomsky Hierarchy

Regular Languages • A language is regular if and only if it is the accepted language of some DFA / NFA • Construct an DFA / NFA for the language described by the regular expression: (ab*a)*

Context-Free Languages • Contains a finite alphabet, S • Contains a finite set of non-terminals, N • S is an element of N and is the Start symbol • R = Rules: Grammar: X sY S = {a,b} X sN = {S} X l R = {S  aSb, S  l} • Uses a stack to hold infinite memory

Context-Sensitive Languages • The number of symbols on the LHS must not exceed the number of symbols on the RHS • A  l is not allowed unless A is the start symbol and does not occur on the RHS of any rule • Since we allow more than one symbol on the LHS, we refer to those symbols other than the one we are replacing as the context of the replacement. • Linear-bounded automaton: a Turing Machine with a finite amount of tape • The syntax of some natural languages (including Dutch, and Swiss German) is held to have structures of this type

Recursively Enumerable • Have no restrictions on their grammar rules (except, of course, that there must be at least one non-terminal on the LHS). • Turing Machine is a finite-state machine in which a transition prints a symbol on a tape. The tape head may move in either direction, allowing the machine to read and manipulate the input as many times as desired. • Predated and provided a model for the design and development of the stored-program computer.

So, why should I care? • Colorless green ideas sleep furiously • Concepts of syntax and semantics used widely in computer science: • Basic compiler functions • Development of computer languages • Exploring the capabilities and limitations of algorithmic problem solving

The Chomskybot • Look On My Words Ye Mighty, And Despair! • I suggested that these results would follow from the assumption that a descriptively adequate grammar does not affect the structure of the strong generative capacity of the theory. If the position of the trace in (99c) were only relatively inaccessible to movement, the natural general principle that will subsume this case cannot be arbitrary in the system of base rules exclusive of the lexicon. To provide a constituent structure for T(Z,K), the speaker-hearer’s linguistic intuition may remedy and, at the same time, eliminate an important distinction in language use. Notice, incidentally, that a case of semigrammaticalness of a different sort suffices to account for problems of phonemic and morphological analysis. It must be emphasized, once again, that this analysis of a formative as a pair of sets of features is not to be considered in determining the requirement that branching is not tolerated within the dominance scope of a complex symbol.

Thank You! • So, you want homework questions, eh? (1.) Construct a parse tree for the grammar: S  aA A  bC C  aS | a (2.) Construct a NFA for (a+b)*b

The Chomsky Hierarchy: Four Computers