An Introduction to Formal Language Theory by Robert N. Moll

By Robert N. Moll

The examine of formal languages and of similar households of automata has lengthy been on the center of theoretical computing device 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 obviously to the next ques­ tions. How may perhaps a grammar be written for this sort of language? How may well we money even if a textual content have been or weren't a well-formed application generated by way of that grammar? How might we parse a software to supply the structural research wanted by means of a compiler? How may well we payment for ambiguity to en­ convinced software has a special research to be handed to the pc? This concentrate on programming languages has now been broadened by way of the in­ creasing situation of laptop scientists with designing interfaces which permit people to speak with desktops in a normal language, not less than bearing on difficulties in a few well-delimited area of discourse. the required paintings in computational linguistics attracts on reports 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 thought typically taught within the context of software­ ming languages with an creation to matters in computational linguistics. it's one in all a chain, The AKM sequence in Theoretical computing device technology, designed to make key mathematical advancements in laptop technological know-how effectively obtainable to undergraduate and starting graduate students.

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Prove: L' regular implies sub(x, L', L) regular. (b) Give an example of an L that is strictly context-free, and an L' that is regular such that sub (x, L, L') is regular. 15. Repeat Example 13 with q2 as the state added last. 1 Push-Down Automata In this section we establish one of the most important equivalences in theoretical computer science: we prove that a language is context-free if and only if some push-down automaton can accept the language in a sense we shall shortly make precise. This result has practical as well as theoretical importance, because a push-down store is the basis for several algorithms used in parsing context-free languages.

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. (a) {aibil i < j} (b) {w E (a + b)*lw has an equal number of a's and b's} (c) the language of matched parentheses 11.

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).

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