An Introduction to Formal Language Theory by Robert N. Moll

By Robert N. Moll

The research of formal languages and of comparable households of automata has lengthy been on the middle of theoretical machine technological know-how. till lately, the most purposes for this centrality have been hooked up with the specification and analy­ sis of programming languages, which led certainly to the subsequent ques­ tions. How may perhaps a grammar be written for this sort of language? How may well we payment even if a textual content have been or weren't a well-formed software generated through that grammar? How may we parse a application to supply the structural research wanted by means of a compiler? How may perhaps we fee for ambiguity to en­ certain application has a special research to be handed to the pc? This specialize in programming languages has now been broadened through the in­ creasing quandary of laptop scientists with designing interfaces which permit people to speak with pcs in a typical language, not less than touching 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 man made intelligence. the current quantity is the 1st textbook to mix the subjects of formal language thought routinely taught within the context of software­ ming languages with an creation to matters in computational linguistics. it's considered one of a sequence, The AKM sequence in Theoretical machine technology, designed to make key mathematical advancements in machine technology without difficulty available to undergraduate and starting graduate students.

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Suppose L = T(M). Modify M by inserting a new stack symbol Z' underneath the usual stack bottom Zo, using the quintuple (qo, A, Zo, qo, ZoZ'). Add a new state qa' and set F, the set of final states, equal to {qa}' Now add the additional rule (q, A, Z', qa' Z') to M, for each state q. The resulting machine will accept L by final state. D Next we consider a modest but useful generalization of the PDA model. 8 Definition. A generalized push-down automaton is a PDA that behaves according to the machine description of Definition 4 except that there may be transitions in {) which read a string of stack symbols (instead of exactly one symbol).

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. 1 Definition. Let X be a finite alphabet. A language L ~ X* is regular if L is finite, or L can be obtained inductively using one of the following operations: (1) Lis L1 u L 2, the union of L1 and L 2, where L1 and L2 are regular; or (2) Lis L1 .

5. Give regular sets corresponding to the following FSAs. 3 Regular and Finite-State Languages 6. Complete the proof of Proposition 16. ) 7. Convert the following NDA into an FSA. 8. , R #- 0. If A. ~ S(R) show that there is an R' such that R' does not mention A. or 0 and S(R) = S(R'). If A. E S(R) show that R = R' + A. where R' does not mention A. or 0. 9. Convert the following regular sets into NDAs. (a) (((11)*0)* + 00)* (b)(1 + 11 + 0)*(00)* 10. Use the pumping lemma for regular sets to show that the following languages are not regular.

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