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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To get a more coherent view on what is going on, and how to fix it, I gladly refer to my latest book Turing Tales [5]. Historical perspective, course syllabus and basic concepts – Lecture 2: Effective computation by humans lsnguages machines.

## Hopcroft and Ullman

Annals of Pure and Applied Logic98 But, of course, if I do that then the much-wanted undecidability result does not hold for linear bounded automata have a decidable halting problem. The former can serve as mathematical models of the latter. Judge for yourself by reading the present post in which I scrutinize the famous textbooks of John E.

Communications of the ACM49 7: The first quote belongs to an introductory chapter on complexity theory where time and space bounds matter while the second quote appears in an informal chapter on Turing machines where the sole distinction of interest is one between decidability and undecidability.

The Creative Partnership of Humans and Technology. 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.

A computer can simulate a Turing machine. Visibly pushdown languages – Lecture Fine with me, but then we are stepping away from a purely mathematical argument. Is the history of computer science solely a history of progress?

### Introduction to Automata Theory, Languages, and Computation

Turing Machines and Computer Programs There is more. But, actually, I have taken each quote out of context. A lot qnd the above remains controversial in mainstream computer science. Morgan Kaufmann, second edition, Not enough citations in the Comm. However, in their Chapter 8, they also attempt to mathematically — albeit informally — demonstrate that a computer can simulate stal Turing machine and that a Turing machine can simulate a computer.

In retrospect, then, both the book and the book bring the same message. Recipes, algorithms, and programs. The emphasis in each quote is mine. Coming then to the simulation of a computer by a Turing machine cf. Automata over unranked trees – Lecture So, to make the undecidability proof work, the authors have decided to model a composite system: Loding, Unranked tree automata with sibling equalities and disequalities.

Lee [9] in order to get the bigger picture.

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. Only if we look at real computers with our traditional spectacles — in which partially computable functions xutomata the preferred objects — can we equate the Turing machine with the computer in a traditional and rather weak sense.

All this in order to come to the following dubious result:. Bounded quantification is undecidable. In this regard, the authors snd draw the following conclusion: At a first glance, both quotes gheory to contradict each other. A separate concern, then, is to discuss and debate how that mathematical impossibility result could — by means of a Turing complete model of computation — have bearing on the engineered artifacts that are being modeled.

However, every now and then Hopcroft et al. Communications of the ACM46 4: Specifically, we should distinguish between two persons:.

### Hopcroft and Ullman | Dijkstra’s Rallying Cry for Generalization

Why interaction is more powerful than algorithms. Automata over ranked finite trees – Lecture A scientist who mathematically models the real computer with a Turing machine. Relating word and tree automataPresented by Zhaowei Xu – Lecture Minds and Machines Chomsky Hierarchy – Overview and Turing machines – Lecture Moreover, modeling implies idealizing: My contention, in contrast, is to view a Turing machine as one possible mathematical model of a computer program.

That, in short, explains why mainstream computer scientists heavily defend the Turing machine as the one and only viable model of computation in an average computability course. The isomorphism that they are considering only holds between Turing machines and their carefully crafted models of real computers. 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.