By Robert N. Moll

ISBN-10: 146139595X

ISBN-13: 9781461395959

ISBN-10: 1461395976

ISBN-13: 9781461395973

The research of formal languages and of similar households of automata has lengthy been on the middle of theoretical laptop technological know-how. until eventually 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 could a grammar be written for any such language? How may we cost even if a textual content have been or weren't a well-formed application generated by means of that grammar? How may perhaps we parse a application to supply the structural research wanted through a compiler? How may possibly we money for ambiguity to en definite software has a distinct research to be handed to the pc? This specialize in programming languages has now been broadened by means of the in creasing challenge of machine scientists with designing interfaces which permit people to speak with pcs in a common language, no less than touching on difficulties in a few well-delimited area of discourse. the required paintings in computational linguistics attracts on reports 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 subjects of formal language thought often taught within the context of software ming languages with an creation to matters in computational linguistics. it really is one among a chain, The AKM sequence in Theoretical machine technological know-how, designed to make key mathematical advancements in desktop technology with ease obtainable to undergraduate and starting graduate students.

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

**Example text**

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).

More formally we proceed as follows. Let G1 and G2 be right-linear grammars. 2 Closure Properties with P7 = {A --+ bBIA --+ bB is in Pd u {A --+ bS21A --+ b is in Pd u P2 is clearly right-linear, and L(G7 ) = Ll . L 2 • ITERATION: Consider the grammar S --+ AI s' s' --+ Sll Sl S'. Then S derives A and Si for n ~ 1. Hence the grammar Gs = (X, VI U {S,S'},S,Ps) with Ps = {S --+ AIS', s' --+ SllSl S'} U PI is context-free if Gl is, and L(Gs ) = Lt. Thus 22 is closed under the * operation. For 20 and 21 we have the same bug as in the prooffor concatenation, and to fix it we adopt the notation and analysis of the concatenation case.

5. For the result on the complement, apply DeMorgan's law again, as in the preceding proof. 0 It turns out that the Type 0 languages are not closed under complement; we will prove this result in Chapter 5. As for the context-sensitive languages, a recently announced result has established that this language class is indeed closed under complement. Next, we look at the effect of substitutions on languages. 6 Definition. } and for each n ~ 1, g(a 1 ••• an) = g(a 1 )g(a2)' .. g(an). That is, g(a 1 ••• an) is built up by concatenating the images of each of the symbols of the string under g.

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