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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Typability and type checking in System F are equivalent and undecidable. References A lot of the above remains controversial in mainstream computer science. Writing Assignment at Siegen University. A much better dissemination strategy, I believe, is to remain solely in the mathematical realm of Turing machines or other — yet equivalent — mathematical objects when explaining undecidability to students, as exemplified by the textbooks of Martin Davis [3, 4].
So there seems to be no problem after all. Furthermore, Hopcroft et al.
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Minds and Machines3: Fundamentals of Theoretical Computer Science. It is not always unproductive, it all depends on the engineering task at hand.
A scientist who eetal models the real computer with a Turing machine.
Moreover, modeling implies idealizing: Note that the modeling in 1. I will argue that to make sense of all this, we need to be explicit about our modeling activities. Automata-theoretical approach to model checking – Lecture In their own words:. The authors are thus definitely not backing up their following two claims:.
Why interaction is more powerful than algorithms. LNCS, Programs are sufficiently like Turing machines that the [above] observations [ Later on in that same chapter fromj.du.llman authors write: Syllabus – Extensive introduction to automata theory and its applications – Automata over finite words, infinite words, finite ranked and unranked trees, infinite trees – Applications: All this in order to come to the following dubious result:.
Bounded quantification is undecidable. My contention is that Turing machines are mathematical objects and computers are engineered artifacts.
Introduction to Automata Theory, Languages, and Computation
In sum, critical readers who resist indoctrination become amused when reading Hopcroft et al. A computer can simulate a Turing machine. Coming then to the simulation of a computer by a Turing machine cf. Thus, we can be confident that something not doable by a TM cannot be done by a real computer. But in the following paragraphs I shall argue that the message conveyed in and again in is questionable and that it has been scrutinized by other software scholars as well. Computability, Complexity, and Languages: However, every now and then Hopcroft et al.
The isomorphism that they are considering only holds between Turing machines and their carefully crafted models of real computers.
Hopcroft and Ullman
In this regard, the authors incorrectly draw the following conclusion: Minds and Machines Chomsky Hierarchy – Regular languages – Lecture Relating word and tree automataPresented by Zhaowei Xu – Lecture 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.
Formal Languages and their Relation to Automata. A Turing machine can mathematically model a computer. Recipes, algorithms, and programs. Physical Hypercomputation and the Church-Turing Thesis. The Coming Software Apocalypse.
Communications of the ACM5: