Get An Introduction to Formal Languages and Automata (3rd PDF

By Peter Linz

ISBN-10: 0763714224

ISBN-13: 9780763714222

An advent to Formal Languages and Automata presents a great presentation of the cloth that's necessary to an introductory concept of computation path. The textual content was once designed to familiarize scholars with the rules and ideas of computing device technological know-how and to bolster the students' skill to hold out formal and rigorous mathematical argument. using a problem-solving process, the textual content offers scholars perception into the direction fabric by means of stressing intuitive motivation and representation of rules via user-friendly factors and strong mathematical proofs. through emphasizing a studying via challenge fixing, scholars research the fabric essentially via problem-type illustrative examples that express the incentive in the back of the options, in addition to their connection to the theorems and definitions.

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Additional info for An Introduction to Formal Languages and Automata (3rd Edition)

Example text

4' fO,) tnir'raa, regula,rexpressiol for I: 12. }, ffi 13, Firxl a regular expressiorrfor f : ,D Iu E {0, I}- : ur has exactly one pair of consecutive zeros} Ctu" rcgular expressiotrsfor the following languages on ( " ) all { o , b ,c } . rrrt,rirrirrgexactly one a, (l') all strings corrtir,itritrg IIL) Illore than three a's, ( c l all strings that contain at least ollc occurreltce of each symbol in r,s ( d ) all str:ings that contain no run of a's of length greater than two, * (") all strings in whir:h all nrrrs of n's have lerrgths that are rrrultiples of three.

A state labeled g represents an impossible move ftrr the nfa and, therefore, means nonacceptance of the string. Conseqrrently, this state in the dfa mrrst be a nonfinal trap state. 12 We have now introduced into the dfa the state {h, qz}, so we need to find the transitions out of this state. Remember that this state of the dfa corresponds to two possible states of the nfa, so we must refer back to the nfa. If the nfa is in state Q1and reads an a, it can go to q1. \-transition to q2. If, for the same input, the nfa is in state q2, then there is no specified transition.

In eachcaseprove that the rcsult rs mlnlmal, (*) fI:{o"b"''n}Z,mlll (b) r : {a"h: n> 0} U {b'a : n } 1} (c) I: { o " o: n ,> 0 , r l l 3 } (d)r: {a^:nt'2 andn+41. ffi is deterministic. 3. du,ce fr) Virri*i"e the states in thc dfa depicteclitr the ftrllowing diagram. L has length at lea^strz, then any dfa accepting -L rnust have at least n, f 1 states. 6. Prove or disprove the following conjecture. L, then M : (Q,E,d,go,Q - f') is a minima,l dfa, for Z. ,* that inrlistinguishability is an equivaletrcerelation but that rlistinguishabilitv is not.

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An Introduction to Formal Languages and Automata (3rd Edition) by Peter Linz

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