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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Introduction to Automata Theory, Languages, and Computation
Is the Church-Turing Thesis True? Automata over infinite words – Lecture Unranked tree automata with sibling equalities and disequalitiesPresented by Xu Gao References – PagesIntroduction to Automata theory, languages and computation J. And then I could rest my case: They are implicitly working with a particular mathematical model of a real computer, not with a real computer itself. References A lot of the above remains controversial in mainstream computer science.
The Dawn of Software Engineering. I don’t j.d.ullmaan so. Historical perspective, course syllabus and basic concepts – Lecture 2: All this in order to come to the following dubious result:. A finite state machine is yet another mathematical model of a computer program. No-nonsense engineers, by contrast, will prefer to use a weaker model of computation and stick to the system at hand: It is not always unproductive, it all depends on the engineering task at hand.
Thomas, Languages, automata and logics, Handbook of formal languages, vol. Fine with me, but then we are stepping away from a llanguages mathematical argument. I recommend consulting the many references provided in my book  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. Typability and type checking in System F are equivalent and undecidable.
Hopcroft and Ullman
Coming then to the simulation of a computer by a Turing machine cf. Automata-theoretical approach to model checking – Autimata In their own words:. Effective computation by humans and machines. Relating word and tree automataPresented by Zhaowei Xu – Lecture Quotes from and I start by comparing the following two quotes. Why interaction is more powerful than algorithms.
In a word, Hopcroft et al. Strachey and ApSimon, My contention is that Turing machines are mathematical objects and computers are engineered artifacts. The J.d.ulpman Partnership of Humans and Technology. Automata theory rormal its applications. Physical Hypercomputation and the Church-Turing Thesis. The authors stick to the Turing machine model and motivate their choice by explaining that computer memory can always be extended in practice:. Bounded quantification is undecidable.
Thus, we can be confident that something not doable by a TM cannot be done by a real computer. Computability, Complexity, and Languages: The authors are thus definitely not backing up their following two claims: Likewise, the latter can serve as engineered models i. 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 atuomata sole distinction of interest is one between decidability and undecidability.
A computer can model i.
Principles of problem solving. Chomsky Hierarchy – Context sensitive and free languages – Lecture I, however, view neither model to be better, for it all depends on the engineering task at hand.
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? So there seems to be no problem after all. Loding, Unranked tree automata with sibling equalities and disequalities.