Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proof systems. SIAM journal on computing, vol. 18 (1989), pp. 186–208. - Oded Goldreich, Silvio Micali, and Avi Wigderson. Proofs that release minimum knowledge. Mathematical foundations of computer science 1986, Proceedings of the 12th symposium, Bratislava, Czechoslovakia, August 25–29, 1986, edited by J. Gruska, B. Rovan, and J. Wiedermann, Lecture notes in computer science, vol. 233, Springer-Verlag, Berlin, Heidelberg, New York, etc., 1986, pp. 639–650. - Oded Goldreich. Randomness, interactive proofs, and zero-knowledge—a survey. The universal Turing machine, A half-century survey, edited by Rolf Herken, Kammerer & Unverzagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988, pp. 377–405.

1991 ◽  
Vol 56 (3) ◽  
pp. 1092-1094
Author(s):  
Lance Fortnow
Keyword(s):  
New York ◽  
Computer Science ◽  
Turing Machine ◽  
Interactive Proof ◽  
Siam Journal ◽  
Proof Systems ◽  
Oxford University ◽  
Universal Turing Machine ◽  
Interactive Proofs ◽  
Mathematical Foundations

Andrew Hodges. Alan Turing and the Turing machine. The universal Turing machine, A half-century survey, edited by Rolf Herken, Kammerer & Unverzagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988. pp. 3–15. - Stephen C. Kleene. Turing's analysis of computahility, and major applications of it. The universal Turing machine, A half-century survey, edited by Rolf Herken, Kammerer & Unverzagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988. pp. 17–54. - Robin Gandy. The confluence of ideas in 1936. The universal Turing machine, A half-century survey, edited by Rolf Herken, Kammerer & Unverzagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988. pp. 55–111. - Solomon Feferman. Turing in the land of O(z). The universal Turing machine, A half-century survey, edited by Rolf Herken, Kammerer & Unverzagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988. pp. 113–147. - Martin Davis. Mathematical logic and the origin of modern computers. The universal Turing machine, A half-century survey, edited by Rolf Herken, Kammerer & Unverzagt, Hamburg and Berlin, and Oxford University Press, Oxford and New York, 1988. pp. 149–174.

1991 ◽  
Vol 56 (3) ◽  
pp. 1089-1090
Author(s):  
John N. Crossley
Keyword(s):  
New York ◽  
Mathematical Logic ◽  
Turing Machine ◽  
Half Century ◽  
Oxford University ◽  
Alan Turing ◽  
Universal Turing Machine ◽  
Martin Davis ◽  
Oxford University Press

A. Bertoni. Mathematical methods of the theory of stochastic automata. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 9–22. - R. V. Freivald. Functions computable in the limit by probabilistic machines. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 77–87. - B. Goetze and R. Klette. Some properties of limit recursive functions. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 88–90. - Ole-Johan Dahl. An approach to correctness proofs of semicoroutines. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 157–174. - G. Wechsung. The axiomatization problem of a theory of linear languages. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 298–302. - L. Banachowski. Modular approach to the logical theory of programs. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 327–332. - Pierangelo Miglioli. Mathematical foundations of motivation languages and synthesis maps. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, edited by A. Blikle, Lecture notes in computer science, vol. 28, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 388–408. - H. Rasiowa. ω+-valued algorithmic logic as a tool to investigate procedures. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974, pp. 423–450. - Andrzej Salwicki. Procedures, formal computations and models. Mathematical foundations of computer science, 3rd symposium at Jadwisin near Warsaw, June 17–22, 1974 pp. 464–484.

1977 ◽  
Vol 42 (3) ◽  
pp. 422-423
Author(s):  
Steven S. Muchnick
Keyword(s):  
New York ◽  
Computer Science ◽  
Modular Approach ◽  
Mathematical Methods ◽  
Logical Theory ◽  
Stochastic Automata ◽  
Correctness Proofs ◽  
Lecture Notes ◽  
Algorithmic Logic ◽  
Mathematical Foundations

Vaughan R. Pratt. Semantical considerations on Floyd–Hoare logic. 17th Annual Symposium on Foundations of Computer Science, Institute of Electrical and Electronics Engineers, New York1976, pp. 109–121. - Michael J. Fischer and Richard E. Ladner. Propositional dynamic logic of regular programs. Journal of computer and system sciences, vol. 18 (1979), pp. 194–211. - Krister Segerberg. A completeness theorem in the modal logic of programs. Universal algebra and applications. Papers presented at Stefan Banach International Mathematical Center at the semester “Universal algebra and applications” held February 15–June 9, 1978, edited by Tadeuz Traczyk, Banach Center Publications, vol. 9, PWN—Polish Scientific Publishers, Warsaw1982, pp. 31–46. - Rohit Parikh. The completeness of propositional dynamic logic. Mathematical foundations of computer science 1978, Proceedings, 7th symposium, Zakopane, Poland, September 4–8, 1978, edited by J. Winkowski, Lecture notes in computer science, vol. 64, Springer-Verlag, Berlin, Heidelberg, and New York, 1978, pp. 403–415. - Dexter Kozen and Rohit Parikh. An elementary proof of the completeness of PDL. Theoretical computer science, vol. 14(1981), pp. 113–118.

1986 ◽  
Vol 51 (1) ◽  
pp. 225-227 ◽  
Author(s):  
Robert Goldblatt
Keyword(s):  
New York ◽  
Computer Science ◽  
Universal Algebra ◽  
Dynamic Logic ◽  
Completeness Theorem ◽  
Theoretical Computer Science ◽  
Propositional Dynamic Logic ◽  
Theoretical Computer ◽  
Mathematical Foundations ◽  
Scientific Publishers

scholarly journals Probabilistic Proof Systems

1994 ◽  
Vol 1 (28) ◽  
Author(s):  
Oded Goldreich
Keyword(s):  
Computer Science ◽  
Essential Role ◽  
International Congress ◽  
Zero Knowledge ◽  
Proof Systems ◽  
Interactive Proofs ◽  
Broad Audience ◽  
Computer Scientists ◽  
Probabilistic Proof

Various types of <em>probabilistic</em> proof systems have played a central role in the development of computer science in the last decade. In this exposition, we concentrate on three such proof systems -- <em>interactive proofs</em>, <em>zero-knowledge proofs</em>, and <em>probabilistic checkable proofs</em> -- stressing the essential role of randomness in each of them.<br /> <br />This exposition is an expanded version of a survey written for the proceedings of the International Congress of Mathematicians (<em>ICM94</em>) held in Zurich in 1994. It is hope that this exposition may be accessible to a broad audience of computer scientists and mathematians.

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