Download An Introduction to Formal Language Theory by Robert N. Moll PDF

By Robert N. Moll

The learn of formal languages and of comparable households of automata has lengthy been on the center of theoretical desktop technological know-how. till lately, the most purposes for this centrality have been attached with the specification and analy­ sis of programming languages, which led evidently to the next ques­ tions. How may possibly a grammar be written for one of these language? How may well we payment even if a textual content have been or weren't a well-formed application generated by means of that grammar? How might we parse a software to supply the structural research wanted through a compiler? How might we payment for ambiguity to en­ certain software has a different research to be handed to the pc? This specialize in programming languages has now been broadened through the in­ creasing hindrance of machine scientists with designing interfaces which enable people to speak with pcs in a usual language, at the least touching on difficulties in a few well-delimited area of discourse. the required paintings in computational linguistics attracts on stories either inside of linguistics (the research of human languages) and inside of man made intelligence. the current quantity is the 1st textbook to mix the themes of formal language idea frequently taught within the context of application­ ming languages with an creation to concerns in computational linguistics. it really is one among a sequence, The AKM sequence in Theoretical desktop technology, designed to make key mathematical advancements in desktop technological know-how effortlessly available to undergraduate and starting graduate students.

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The baU) PP /\ I I Prep NP on? ". A large body oflinguistic theory is concerned with characterizing the ways in which such apparently non-con text-free distortions can happen. , a prepositional phrase with empty object) that clearly form an integral part of natural language. We shall develop one such description in Chapter 9. 5 1. " 2. Using the top-down algorithm ofthe last section, describe how you might parse the sentence in Exercise 1. 3 Regular and Finite-State Languages In Chapter 1 we had a first look at context-free grammars and context-free languages, and we had a glimpse at two areas of practical interest-parsing and natural language processing-where formal grammatical descriptions play an important role.

Consider the language {wlw E (a + b)*, w has an equal number of a's and b's}. This language is informally acceptable by a stack using the following algorithm. Initially the stack is empty. 1 Push-Down Automata T -Stack top N Stack Figure 1 "Pop" pops T ofT stack, leaving N on top. "Push A" pushes A on top, moving T to second position. (1) if the stack is empty and the current symbol ofw is an a, put A on the stack; (2) if the stack is empty and the current symbol of w is a b, put B on the stack; (3) if the top stack symbol is an A and the current symbol of w is an a, push another A onto the stack; (4) if the top stack symbol is a B and the current symbol ofw is a b, push a B onto the stack; (5) if the top stack symbol is an A and the current symbol of w is a b, pop the stack; (6) if the top stack symbol is a B and the current symbol of w is an a, pop the stack.

3 1. Describe in words the languages specified by the following regular expressions: (a) (aa)*(bb)* (b) (a*b*e*)* (c) «a + b + e)(bb)* + (a + b + e))* (d) (aaa + aaaaa)* 2. Show that the following equivalences hold for arbitrary regular expressions R, S, and T: (a) R . (8 + T) (b) (R + S)· T = R . 8 + R· T = R . S + R· T 3. , S·R 4. Give a right-linear grammar for the language «a + bb)* + e)*. 5. Give regular sets corresponding to the following FSAs. 3 Regular and Finite-State Languages 6. Complete the proof of Proposition 16.

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