By Robert N. Moll

The research of formal languages and of comparable households of automata has lengthy been on the center of theoretical machine technology. until eventually lately, the most purposes for this centrality have been hooked up with the specification and analy sis of programming languages, which led evidently to the subsequent ques tions. How may perhaps a grammar be written for this sort of language? How may well we cost no matter if a textual content have been or weren't a well-formed application generated through that grammar? How may well we parse a application to supply the structural research wanted by means of a compiler? How may perhaps we money for ambiguity to en yes software has a different research to be handed to the pc? This concentrate on programming languages has now been broadened by way of the in creasing obstacle of desktop scientists with designing interfaces which permit people to speak with desktops in a usual language, at the least bearing on difficulties in a few well-delimited area of discourse. the mandatory paintings in computational linguistics attracts on experiences either inside linguistics (the research of human languages) and inside of man made intelligence. the current quantity is the 1st textbook to mix the subjects of formal language concept generally taught within the context of software ming languages with an advent to concerns in computational linguistics. it really is one in all a chain, The AKM sequence in Theoretical machine technological know-how, designed to make key mathematical advancements in desktop technology conveniently available to undergraduate and starting graduate students.

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**Extra info for An Introduction to Formal Language Theory**

**Sample text**

3 Regular and Finite-State Languages In this section we present an algebraic description of right-linear languages as the languages denoted by regular expressions. Then we introduce a machinetheoretic approach to these languages by showing that the right-linear languages are precisely those accepted by finite-state acceptors. The equivalence of these three characterizations is the principal result concerning right-linear languages. We prove this result, which is known as Kleene's theorem, in this section.

Vn)*) with wli . lwmlw1BI ... lwmB o One final point: notice that the new variable, B, never appears as the leftmost symbol in any production of the new grammar. This will be an important fact in the proof of the next result, which establishes that every context-free language has a Greibach normal form.

We 48 3 Push-Down Automata and Context-Free Grammars must therefore introduce the "A-rule" (7) which, on no input, erases the bottom marker Zoo We say a string is accepted if after the string has been completely scanned, the stack is empty. 2 Example. Consider the language {wcwRlw E (a + b)*}. This language, as we shall see, is recognizable by an automaton of the kind in the last example, but a more convenient way to recognize it is to augment the stack machinery with a finite-state structure consisting of two states, one called read for processing the first half of the string, the other, called match, for the second half.