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  J.E. Hopcroft, R. Motwani, and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison Wesley / Pearson Education,  J.E. Hopcroft and J.D. Ullman. Formal Languages and their Relation to Automata.
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Not enough citations in the Comm. Moreover, is it not possible that if we look inside a real computer and refrain theorj 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?
Moreover, modeling implies idealizing: The Dawn of Software Engineering.
Hopcroft and Ullman
Minds and Machines3: Annals of Pure and Applied Logic98 The former can serve as mathematical models of the latter. In their own words: I don’t think so. 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 . Communications of the ACM49 7: Chomsky Hierarchy – Context sensitive and free languages – Lecture Lee  in order to get the bigger picture.
Based on their motivations not to use finite state machines, I would opt for a linear bounded automaton and not a Turing machine. Physical Hypercomputation and the Church-Turing Thesis. My contention, in contrast, is to view a Turing machine as one possible mathematical model of a computer program. A finite state machine is yet another mathematical model of a computer program. Automata for XML – Lecture 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.
A lot of the above remains controversial in mainstream computer science.
Hopcroft and Ullman | Dijkstra’s Rallying Cry for Generalization
The authors stick to the Turing machine model and motivate their choice by explaining that computer memory can always be extended in practice: Communications of the ACM40 5 A computer can simulate a Turing machine. Turing Machines and Computers J.d.uloman contention is that Turing machines are mathematical objects and computers are engineered artifacts.
However, every now and then Hopcroft et al. Computation beyond Turing machines. Computability, Complexity, and Languages: No-nonsense engineers, by contrast, will prefer to use a weaker model of computation and stick to the system at hand: In sum, critical readers who resist indoctrination become amused when reading Hopcroft et al.
So there seems to be no problem after all.
Laguages the Church-Turing Thesis True? The previous statement only holds if the authors have demonstrated an isomorphism between Turing machines on the one tyeory and real computers on the other hand. Note that the modeling in 1. Cars and Automatic Programming. So, to make the undecidability proof work, the authors have decided to model a composite system: Automata over ranked finite trees – Lecture And then I could rest my case: My contention is that Turing machines are mathematical objects and computers are engineered artifacts.