Read e-book online A second course in formal languages and automata theory PDF

By Jeffrey Shallit

ISBN-10: 0511438354

ISBN-13: 9780511438356

ISBN-10: 0521865727

ISBN-13: 9780521865722

Meant for graduate scholars and complex undergraduates in desktop technological know-how, A moment direction in Formal Languages and Automata conception treats subject matters within the thought of computation now not often lined in a primary path. After a evaluate of uncomplicated recommendations, the e-book covers combinatorics on phrases, standard languages, context-free languages, parsing and popularity, Turing machines, and different language periods. Many issues frequently absent from different textbooks, comparable to repetitions in phrases, kingdom complexity, the interchange lemma, 2DPDAs, and the incompressibility technique, are lined right here. the writer locations specific emphasis at the assets had to characterize convinced languages. The ebook additionally encompasses a varied number of greater than 2 hundred workouts, feedback for time period tasks, and examine difficulties that stay open.

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Proof. Let us assume that this problem, called the halting problem, is solvable. This means that there exists a TM, call it MH , that takes an input of the form e(T )e(w) and eventually halts, writing 1 on its output tape if T halts on w and 0 otherwise. 6. 7: Constructing TM ML from MH Now let us create a new TM ML as follows: it simulates MH and then examines the tape after MH halts. , by moving right on every tape symbol). If the tape contains a 0, then ML halts. 7. Finally, we make a new TM MD as follows: on input e(T ), MD computes the encoding of e(T ), that is, e(e(T )), and writes it on the tape after e(T ).

2. SAT is NP-complete. Proof Idea. It is easy to see that SAT is in NP, for all we need do is guess a satisfying assignment and then verify it. To show that every problem in NP reduces to SAT, take a polynomial-time-bounded TM M. 9 Exercises August 6, 2008 21:1 21 an input x to a Boolean formula ϕx , such that ϕx is satisfiable if and only if M accepts x. We encode the computation of M on x as a string s of configurations separated by delimiters and then create Boolean variables ci,a that are true if and only if the ith symbol of s equals a.

1 The book of Perrin and Pin [2003] is a very good source of information on infinite words. 2 Harju and Karhum¨ aki [1997] is an excellent discussion of morphisms. 3, see Lyndon and Sch¨ utzenberger [1962]. 5 is a new generalization of a classical theorem of Fine and Wilf [1965]. 3. Some of the material of this section was taken essentially verbatim from Allouche and Shallit [2003], with permission of Cambridge University Press. 2 is due to Shyr and Thierrin [1977]. 5 is from Lyndon and Sch¨ utzenberger [1962].

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A second course in formal languages and automata theory by Jeffrey Shallit

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