Zhang, J.: Search for idempotent models of quasigroup identities, Typescript, Institute of Software, Academia Sinica, Beijing, 1991. 6  Home/Search   Document Not in Database   Summary   Related Articles   Check

....particular, are there such quasigroups of order 9, 10, 12, 13, 14, 15 or 16 This was the first problem we investigated, and for no especially good reason we have invested more effort in it than in the others. The order 9 (idempotent) case had already been solved negatively by Jian Zhang in 1990 [13] and his result confirmed by us in 1991 using an earlier version of FINDER. MGTP obtained new negative results for order 12 (idempotent) and for order 10 (without assumption of idempotence) Larger idempotent cases have been examined since then. DDPP showed in 1992 that there is no model of ....

J. Zhang, Search for Idempotent Models of Quasigroup Identities, Typescript, Institute of Software, Academia Sinica, Beijing.

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Zhang, J.: Search for idempotent models of quasigroup identities, Typescript, Institute of Software, Academia Sinica, Beijing, 1991. 6

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Zhang, J. Search for idempotent models of quasigroup identities, Typescript, Institute of Software, Academia Sinica, Beijing. 1990. 18

....used in our programs. One of the major motivations for developing our programs was to solve open problems in algebra concerning the existence of quasigroups satisfying certain constraints [1] The usefulness of computer programs to attack these quasigroup problems has been demonstrated in [19, 8, 15]. We prefer these quasigroup problems as benchmarks over randomly generated SAT problems for testing constraint solving methods: The problems have fixed solutions; descriptions of the problems are simple and easy to communicate; most important, some cases of the problems remain open, offering ....

Zhang, J.: Search for idempotent models of quasigroup identities, typescript, Institute of Software, Academia Sinica, Beijing,

....developing our programs is to attack open quasigroup problems in algebra (Bennett and Zhu, 1992) The theory of quasigroup contains many hard computational problems. The usefulness of advanced automated reasoning techniques in attacking these quasigroup problems was successfully demonstrated in Zhang (1990), Fujita et al. 1993) Slaney et al. 1995) and Zhang and Stickel (1994) Several open problems were solved using the approach described in this paper; other reasoning systems have not been able to reproduce many of these results. Because the SAT problem is the first known NP complete problem, ....

....are easy to communicate. More importantly, open problems in quasigroups have attracted the interest of several researchers and became a challenge for friendly competition. The usefulness of general automated reasoning techniques to attack these quasigroup problems was successfully demonstrated in Zhang (1990), Fujita et al. 1993) Zhang (1993) Slaney et al. 1995) Zhang and Stickel (1994) and McCune (1994) To our knowledge, J. Zhang was the first to use a general reasoning program to solve an open case of the quasigroup problems. Subsequently, Fujita used MGTP, a model generation based first order ....

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Zhang, J., (1990) Search for idempotent models of quasigroup identities. Preprint, Institute of Software, Academia Sinica, Beijing.

....in algebra [1] The usefulness of computer programs to attack these Partially supported by the National Science Foundation under Grants CCR 9202838 and CCR 9357851. y Research supported by the National Science Foundation under Grant CCR 8922330. quasigroup problems has been demonstrated in [16, 7, 14]. We think these quasigroup problems are much better benchmarks than randomly generated SAT problems for testing constraint solving methods: the problems have fixed solutions; descriptions of the problems are simple and easy to communicate; most importantly, some cases of the problems remain open, ....

Zhang, J. Search for idempotent models of quasigroup identities. Typescript, Institute of Software, Academia Sinica, Beijing.

....a subsquare (which itself is also a Latin square) of the square is missing. Quasigroups raise many combinatorial problems, some of which are often approached computationally. The usefulness of advanced automated reasoning techniques to attack these problems have been successfully demonstrated in [11, 3, 7, 10, 6]. In 1990, Zhang reported a case of open problems in quasigroups solved using a constraint solving technique [11] Subsequently, Fujita used MGTP, a model generation based first order theorem prover, and Slaney used FINDER, a program based on constraint solving, to solve several open problems in ....

....of which are often approached computationally. The usefulness of advanced automated reasoning techniques to attack these problems have been successfully demonstrated in [11, 3, 7, 10, 6] In 1990, Zhang reported a case of open problems in quasigroups solved using a constraint solving technique [11]. Subsequently, Fujita used MGTP, a model generation based first order theorem prover, and Slaney used FINDER, a program based on constraint solving, to solve several open problems in quasigroups [3] Later, Stickel and Zhang, independently, used their proposi Table 1: Some constrains of ....

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Zhang, J. Search for idempotent models of quasigroup identities, manuscript, Institute of Software, Academia Sinica, Beijing. 1990.

....the major motivation for developing our programs is to attack some open quasigroup problems in algebra [1] Quasigroup problems raise many hard computational problems. The usefulness of advanced automated reasoning techniques in attacking these quasigroup problems was successfully demonstrated in [14, 5, 11, 13]. Several open problems were solved using the approach described in this paper; other reasoning systems have not been able to reproduce these results. This paper is organized as follows: the next section introduces SATO and provides a solution on how to cumulate the search effort of SATO based on ....

....are easy to communicate. Most important, some open cases of these problems attracted the interest of several researchers and became a challenge for friendly competition. The usefulness of general automated reasoning techniques to attack these quasigroup problems was successfully demonstrated in [14, 5, 11, 13, 9] To our knowledge, Zhang [14] was the first to use a general reasoning program to solve an open case of the quasigroup problems. Subsequently, Fujita used MGTP, a model generation based first order theorem prover, and Slaney used FINDER, a program based on constraint solving, to solve several open ....

[Article contains additional citation context not shown here]

J. Zhang. Search for idempotent models of quasigroup identities. Typescript, Institute of Software, Academia Sinica, Beijing, 1990.

....To illustrate the importance of the specification techniques, let us consider the nonexistence problem of idempotent Latin square of order 9 satisfying the constraint ( y x) y) y = x. J. Zhang was the first to solve this problem, in 1990, using his model generator FALCON [21]. In [17] we reported that SATO confirmed this result after spending 25 CPU hours on a Sparc 2 workstation. The latest version of SATO can do the same in 20 minutes, with the plain specification of the problem. Applying the techniques to be described in this chapter to the same problem, SATO can ....

Zhang, J.: Search for idempotent models of quasigroup identities, typescript, Institute of Software, Academia Sinica, Beijing, 1991.

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