Christoph Kreitz. Constructive automata theory implemented with the Nuprl proof development system, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....allow DA.accepts to operate in time linear in the size of the input string. Scanning, however, is quadratic, because the recognition of each maximal prefix requires traversing the whole (remaining) string. 7 Related work I am aware of three other papers on formalized automata theory [7, 4, 2], all of which use constructive type theory (i.e. they extract their algorithms from the proofs rather than providing them as part of the definitions) and follow [6] closely. The main result of Kreitz [7] is the pumping lemma and the main result of Constable et al. 2] the Myhill Nerode theorem. ....

....string. 7 Related work I am aware of three other papers on formalized automata theory [7, 4, 2] all of which use constructive type theory (i.e. they extract their algorithms from the proofs rather than providing them as part of the definitions) and follow [6] closely. The main result of Kreitz [7] is the pumping lemma and the main result of Constable et al. 2] the Myhill Nerode theorem. Both of them use the Nuprl system. Closest to our work is that by Filliatre [4] who gives a constructive proof for the translation of regular expressions into nondeterministic finite automata with moves ....

C. Kreitz. Constructive automata theory implemented with the Nuprl proof development system. Technical Report TR 86-779, Dept. of Computer Science, Cornell University, 1986.

....in this book (pages 29 34) especially the construction of the finite automaton corresponding to a regular expression with three different kinds of finite automata. It is important to say here that such a formalization had been previously done in the Nuprl system [3] by Christoph Kreitz in 1986 [11]. The main result is a constructive proof a the pumping lemma (for any finite automaton A, there exists a natural number n such that any word w of length n recognized by A is of the form xyz with jxyj n, jyj 1 and xy i z recognized by A for any i 0) The computational meaning of this proof, ....

C. Kreitz. Constructive Automata Theory Implemented with the Nuprl Proof Development System. Technical Report TR 86--779, Cornell University, Department of Computer Science, September 1986.

....Howe used Nuprl to prove the fundamental theorem of arithmetic[12] and Girard s paradox[13] Cleaveland developed the synchronization tree This research was supported in part by NSF grants CCR8502243 and DCR8303327. model of CCS[3] and Kreitz proved theorems in constructive automata theory[15]. This author has used Nuprl to develop an environment for proving theorems in recursion theory[1] and has recently proved Ramsey s theorem. Mathematical development in completely formal systems is a relatively new enterprise starting in 1968 with Automath[7] A number of systems exist today ....

Christoph Kreitz. Constructive automata theory implemented with the Nuprl proof development system. Technical Report 86-779, Cornell University, 1986.

....of deterministic Muller machines, and can convert these machines into regular expressions. FADELA also supports other operations on machines including minimization and complement. An interesting experience is the development of machine tools in Nuprl, a proof language based on the lambda calculus[9]. Definitions were constructed in Nuprl for finite sets, strings, tuples, and deterministic machines. Nuprl was then able to construct a proof of the pumping lemma. The main point of this work was not the development of an environment for manipulating machines, but an illustration of the utility ....

C. Kreitz, "Constructive Automata Theory Implemented with the Nuprl Proof Development System," Technical report TR-86-779, Department of Computer Science, Cornell University, Ithaca, New York (September 1986).

....the impact of a knowledge base on the formalization task. Because it required building new basic material about the quotient type, we see why formalization efforts are so laborious. 6. The existence of an earlier formalization of the pumping lemma from automata theory by Christoph Krietz in 1988 [23] in Nuprl 3 allows us to compare the progress made in the tactic collection from version 3 (1988) to version 4.2 (1995) 7. Finally, the formalization reveals some technical problems about how to formalize computational mathematics. The question involves reasoning about quotient sets, and it is a ....

C. Kreitz. Constructive automata theory implemented with the Nuprl proof development system. Technical Report 86-779, Cornell University, Ithaca, New York, September 1986.

....on several levels of interface (process, function library, object) AMORE and AUTOMATE appear to be monolithic programs that attempt to provide a single interface to the user. One interesting experience is the development of automata tools in Nuprl, a proof language based on lambda calculus[11]. Definitions were constructed in Nuprl for finite sets, strings, tuples, and deterministic automata. Nuprl was then able to construct a proof of the pumping lemma. The main point of this work was not the development of an environment for manipulating automata, but an illustration of the utility ....

Christoph Kreitz, "Constructive Automata Theory Implemented with the Nuprl Proof Development System," Technical report TR-86-779, Department of Computer Science, Cornell University, Ithaca, New York (September 1986).

....the formalization on the presentation in the book cited above. We chose this theorem because it is one of the first significant theorems in the book, and because it involves computationally interesting constructions. Automata theory was previously explored in Nuprl by Christoph Kreitz in 1986 [22]. In particular, he proved the pumping lemma for finite automata. We saw that we needed this lemma for our constructivization of the MyhillNerode theorem, and so reproved it using Nuprl s current tactic collection. We therefore could compare the currently achievable level of automation with that ....

C. Kreitz. Constructive automata theory implemented with the Nuprl proof development system. Technical Report 86-779, Cornell University, Ithaca, New York, September 1986.

....to write meta programs guiding the application of refinement rules. Such tactics act as derived inference rules whose correctness is guaranteed by the fact that they have to make use of primitive inference rules to actually modify a proof. Experiments with NuPRL reported in [CAB 86, How86, Kre86, Cle87, How88a, Bas89] show that together with the expressive power of Type Theory these components strongly support a flexible high level implementation of mathematical theories. 3 Methodology and notation As said before the formal theory of program construction shall provide a unified ....

....which an algorithm design system needs to fulfil its task. Formal definitions introduce new notions. In formal theorems important properties are stated and verified. During the past years, a number of domain theories have been implemented with NuPRL. We refer the reader to [CAB 86, How86, Kre86, Cle87, How88a] and particularly to [Bas89] for accounts of how mathematical knowledge should be represented and reasoned about. Here we will present some elements of a theory about finite sets over ordered types which we will use in Section 4.3. The Set constructor yields for every type T the ....

C. Kreitz. Constructive automata theory implemented with the NuPRL proof development system. Report TR 86-779, Cornell University. Department of Computer Science, 1986.

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Christoph Kreitz. Constructive automata theory implemented with the Nuprl proof development system, 1986.

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C. Kreitz. Constructive automata theory implemented with the Nuprl proof development system. Technical Report 86--779, Cornell University, Ithaca, New York, September 1986.

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