Read e-book online An Introduction to Formal Language Theory PDF

By Robert N. Moll

ISBN-10: 146139595X

ISBN-13: 9781461395959

ISBN-10: 1461395976

ISBN-13: 9781461395973

The examine of formal languages and of comparable households of automata has lengthy been on the middle of theoretical desktop technology. till lately, the most purposes for this centrality have been hooked up with the specification and analy­ sis of programming languages, which led clearly to the subsequent ques­ tions. How may perhaps a grammar be written for this sort of language? How might we cost no matter if a textual content have been or weren't a well-formed application generated by way of that grammar? How may we parse a software to supply the structural research wanted via a compiler? How may we cost for ambiguity to en­ certain application has a different research to be handed to the pc? This specialise in programming languages has now been broadened by way of the in­ creasing challenge of computing device scientists with designing interfaces which enable people to speak with pcs in a typical language, at the very least pertaining to difficulties in a few well-delimited area of discourse. the mandatory paintings in computational linguistics attracts on reviews either inside linguistics (the research of human languages) and inside man made intelligence. the current quantity is the 1st textbook to mix the themes of formal language concept commonly taught within the context of software­ ming languages with an advent to matters in computational linguistics. it's considered one of a chain, The AKM sequence in Theoretical computing device technological know-how, designed to make key mathematical advancements in laptop technology without problems available to undergraduate and starting graduate students.

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Thus we begin with b a which describes the action of (j' on the initial state {81 , 8 2 } of inputs a and b, respectively. Only one new state has been generated, so we next produce its row: b a Then we get {A} a b {A} {A} and we are done. 3 Regular and Finite·State Languages We have now developed enough machinery to prove that every right·linear language can be represented by T(M) for some finite state acceptor M. 18 Theorem. Every right-linear language L is a FSL. PROOF. Let L = L(G) where G = (V, X, S, P) is a right-linear grammar.

It will turn out that the "pure" notion of a stack described informally above, augmented by the notion of nondeterministic state transition, provides a complete acceptor model for context-free languages. However, certain additional structure is also convenient, and the next three examples show why this is so. 1 Example. 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.

Then, considering all pairs A, B of variables, if A ~ B according to P, we also include in P' all productions of the form A -+ w where B -+ w is a production of P and w ¢ V. We leave as an exercise the proof that L(G) = L(G'). 0 2 Definition. We say that a context-free grammar G = (V, X, S, P) is in Chomsky normal form if each production is of one of the following forms: (i) S -+ A, (ii) A -+ BC, where A, B, C E V, (iii) A -+ a, where A E V and a E X. Furthermore, if S -+ A is in P, then B, C E V - {S} in clause (ii).

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