An Introduction to Formal Languages and Automata, 5th Edition

An Introduction to Formal Languages and Automata, 5th Edition

Language: English

Pages: 437

ISBN: 144961552X

Format: PDF / Kindle (mobi) / ePub

Written to address the fundamentals of formal languages, automata, and computability, An Introduction to Formal Languages and Automata provides an accessible, student-friendly presentation of all material essential to an introductory Theory of Computation course. It is designed to familiarize students with the foundations and principles of computer science and to strengthen the students' ability to carry out formal and rigorous mathematical arguments. In the new Fifth Edition, Peter Linz continues to offer a straightforward, uncomplicated treatment of formal languages and automata and avoids excessive mathematical detail so that students may focus on and understand the underlying principles. In an effort to further the accessibility and comprehension of the text, the author has added new illustrative examples and exercises throughout. There is a substantial amount of new material in the form of two new appendices, and a CD-ROM of JFLAP exercises authored by Susan Rodger of Duke University. The first appendix is an entire chapter on finite-state transducers. This optional chapter can be used to prepare students for further related study. The second appendix offers a brief introduction to JFLAP; an interactive software tool that is of great help in both learning the material and in teaching the course. Many of the exercises in the text require creating structures that are complicated and that have to be tested for correctness. JFLAP can greatly reduce students’ time spent on testing as well as help them visualize abstract concepts. The CD-ROM that accompanies every new printed copy expands this and offers exercises specific for JFLAP. (Please note, ebook version does not include the CD-ROM) Instructor Resources: -Instructor Manual -PowerPoint Lecture Outlines

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only if the original nfa accepts u. Therefore, the modified nfa accepts .Lft, proving closure under reversaJ. t 4.1 CI,osuRr.: Pn,opnnrrnsor R,tcuu,R LAN(+rrAGEs 103 ClosureunderOtherOperotions In acldition to the standarcl operations on la,nguarges,orre ca,rl dclirre other operatiorrs atrd investigatc closure propertics for thenr. Thr:re are ma,ny srrr:h results; we select only two typical ones. Others are explored in the exrlrc:ises at tht: crrd of this sectitxr. ' 1i',,

trt, ot tells us that nrr parsing is possible. Proof; For each sentential forrrt, consider both its length and the number of terminal synrbols. Each step in the derivation increases at lcir"st one of these. Since neither the lerreth of a senterrtial form nor the rrtrmber of 5.2 Pansruc ANDAMBrcurrtr 1SS tertninal symbols can excced lrul, a derivation carrnot involve rlore thtr.n 2 lul rorruds, at wlfch ti're we either havera succerssfulparsing or .u cannot bc genertr.tedby the gra,rrrrrar. I

sutlstituticxrs thu,t will bc rrscfirl irr srrbsr:tlrrclrrt rlisrlrssiorrs. \A/tl alstl irrvt:stigtrtc rrorrnal forrrrs f'rlr cxirrtr:xt-fr(xi grarrrrrrars, A 1orrnal filrrn is orrt: tlurt, a,lthough rr:strir:tc:rl,is llroad errough so that, a1y glirrrlrrlirr hlm itrr tx|rivirlertt trorrrtirl-forrrr versiorr. We itrtroduce two of the tnost useful of these, the chomsky norrnal form ancl the Greibach normal form. .Both ltave tnatr.ypractical and theoretical uses. An immecliate applicalion of the

(")l l c ls(?z)l then / has order at least g, I'rrr whit:h we tuJe /(") :o(g(")), Finar,lly,if there exist constants c1 and c2 such tlnt cr lg(?l)l< l/ (")l ! czle(rl)l, / and g have the same ordcr of magnitude, expresseda,s I(n)*o(g("))' In this order of magtritude trotittitlrr, wtr ignore multiplicative constants and lower order tertns that becotnencgligibkl as n increases. ExompleI.3 Let f (n) : 2nz + iJtt,, I (rt) : "'t, h , ( n ) : 1 o r z+2 1 o o . Thcn / (t) : o (s (rl)). s (n) : o

is the current state of the: pda, while the sequenceof middle symbols is the same as the stack content. Although the construction yields a rather complicated grammar, it can be applied to any pda whose transition rules satisfu the given conditions. This forms the basis for the proof of the general result. I Iffi language' u h: r(:r,r)lforsoqenpdaM, then.Lis a context-free Proof: Asslrme that M : (8,X,f,d,S,1,2,{gl}) satisfies conditions 1 and 2 above. We use the suggested construction to get

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