New PDF release: Automata and Computability (Undergraduate Texts in Computer

By Dexter C. Kozen

ISBN-10: 0387949070

ISBN-13: 9780387949079

This textbook presents undergraduate scholars with an creation to the elemental theoretical types of computability, and develops a few of the model's wealthy and sundry constitution. the 1st a part of the publication is dedicated to finite automata and their homes. Pushdown automata supply a broader category of types and allow the research of context-free languages. within the last chapters, Turing machines are brought and the booklet culminates in analyses of potent computability, decidability, and Gödel's incompleteness theorems. scholars who have already got a few adventure with trouble-free discrete arithmetic will locate this a well-paced first path, and a couple of supplementary chapters introduce extra complicated concepts.

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Extra resources for Automata and Computability (Undergraduate Texts in Computer Science)

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This is the nondeterministic analog of the construction of (; for deterministic automata we have already seen. Note that for a E E, &(A,a) = U ~(p,a) PEa(A,<) = U ~(p,a). pEA The automaton N is said to accept x E E* if &(8,x)nF:;60. , q E &(8, x)). We define L(N) to be the set of all strings accepted by N: L(N) = {x E E* I N accepts x}. 34 Lecture 6 Under this definition, every DFA (Q, E, 8, s, F) is equivalent to an NFA (Q, E, ~, {s}, F), where ~(p,a) ~ {8(p, a)}. Below we will show that the converse holds as well: every NFA is equivalent to some DFA.

Add a new state s. Add f-transitions from s to all the start states of M and from all the final states of M to s. Make s the only start state of P and also the only final state of P (thus the start and final states of M are not start and final states of P). Then P accepts exactly the set A*. 8 Let A = {aa}. 7. Here is the automaton you get for A * by the construction above: ~iE .. f a •• o In this construction, you must add the new start/final state s. You might think that it suffices to put in E-transitions from the old final states back to the old start states and make the old start states final states, but this doesn't always work.

And f3 are equivalent? Sometimes it is obvious and sometimes not. • Which operators are redundant? For example, we can get rid of E since it is equivalent to "'(#@) and also to fij*. We can get rid of@ since it is equivalent to #*. *. We can get rid of #, since if E = {ab ... ,an} then # is equivalent to the pattern Pattern Matching and Regular Expressions 45 The operator n is also redundant, by one of the De Morgan laws: 0: n 13 is equivalent to "" ("" 0: + "" 13). Redundancy is an important question.

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Automata and Computability (Undergraduate Texts in Computer Science) by Dexter C. Kozen

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