I have prepared a course in automata theory (finite automata, context-free grammars, decidability, and intractability), and it begins April 23, You can learn. Why Study Automata Theory? § Introduction to Formal Proofs Dantsin, E. et al. (). Automata theory, Languages, and Computation. 3rd ed. Pearson. Hopcroft et al. also essentially equate Turing machines and [7] J.E. Hopcroft, R. Motwani, and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison Wesley / Pearson Education, [8] J.E. Hopcroft and J.D. Ullman. Formal Languages and their Relation to Automata.

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The writings of Robert Floyd [6], Benjamin Pierce [10], and Joe Wells [16], just to give three names, show that undecidability most definitely has a practical role to play when used properly. Syllabus – Extensive introduction to automata theory and its applications – Automata over finite words, infinite words, finite ranked and unranked trees, infinite automzta – Applications: I recommend consulting the many references provided in my book [5] and also the related — but not necessarily similar — writings of Peter Wegner [13, 14, 15], Carol Cleland [1, 2], Oron Shagrir [11, 12], and Edward A.

So there seems to be no problem after all. Based on their motivations not to use finite state machines, I would opt for a linear bounded automaton and not a Turing machine.


Lee [9] in order to get the bigger picture. Furthermore, Hopcroft et al. It is not always unproductive, it all depends on the engineering task at hand. Hopcroft and Jeffrey D. LNCS, In this regard, the authors incorrectly draw the following conclusion:. Only if we look at real computers with our traditional spectacles — in which partially computable functions are the preferred objects — can we equate the Turing machine with the computer in a traditional and rather weak sense.

Coming then to the simulation of a computer by a Turing machine cf. Turing Machines and Computers My contention is that Turing machines are mathematical objects and computers are engineered artifacts.

Introduction to Automata Theory, Languages, and Computation

In retrospect, then, both the book and the book bring the same message. I don’t think so.

Moreover, is it not possible that if we look inside a real computer and refrain from mapping our observations onto our favorite mathematical objects, that the computer is, in some sense, doing something for us that Turing machines do not do?

Physical Hypercomputation and the Church-Turing Thesis. Note that the modeling in 1.

Tree-walking automata do not recognize all regular languages. The authors are thus definitely not backing up their following two claims:. A finite thoery machine is yet another mathematical model of a computer program.


Hopcroft and Ullman

Why interaction is more powerful than algorithms. Typability and type checking in System F are equivalent and undecidable. An engineer who models i.

Bounded quantification is undecidable. In a word, Hopcroft et al.

Communications of the ACM49 7: But, actually, I have taken each quote out of context. The isomorphism that they are considering only holds between Turing machines and their carefully crafted models of real computers. The previous statement only holds if the authors have demonstrated an isomorphism between Turing machines on the one hand and real computers on the other hand.

Reading Assignments at Siegen University. The authors stick to the Turing machine model and motivate their choice by explaining that computer memory can always be extended in practice:. At a first glance, both quotes seem to contradict each other. Specifically, we should distinguish between two persons:. Principles of problem solving.