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COMPUTATIONALLY AND ALGEBRAICALLY COMPLEX FINITE ALGEBRA MEMBERSHIP PROBLEMS
"... Abstract. In this paper we produce a finite algebra which generates a variety with a PSPACEcomplete membership problem. We produce another finite algebra with a γ function that grows exponentially. The results are obtained via a modification of a construction of the algebra A(T) that was introduced ..."
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(T) that was introduced by Ralph McKenzie in 1996. 1.
Problems and results in tame congruence theory  A survey of the '88 Budapest Workshop
 Algebra Universalis
, 1992
"... . Tame congruence theory is a powerful new tool, developed by Ralph McKenzie, to investigate finite algebraic structures. In the summer of 1988, many prominent researchers in this field visited Budapest, Hungary. This paper is a survey of problems and ideas that came up during these visits. It is ..."
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. Tame congruence theory is a powerful new tool, developed by Ralph McKenzie, to investigate finite algebraic structures. In the summer of 1988, many prominent researchers in this field visited Budapest, Hungary. This paper is a survey of problems and ideas that came up during these visits
On McKenzie’s method
 Per. Math. Hungar
, 1996
"... Dedicated to Lászlo ́ Fuchs on the occasion of his 70th birthday This is an expository account of R. McKenzie’s recent refutation of the RS conjecture. We adopt the usual conventions: if S is an algebra then S denotes the universe of S, S  denotes the cardinality of S, and S+ denotes the succes ..."
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Dedicated to Lászlo ́ Fuchs on the occasion of his 70th birthday This is an expository account of R. McKenzie’s recent refutation of the RS conjecture. We adopt the usual conventions: if S is an algebra then S denotes the universe of S, S  denotes the cardinality of S, and S+ denotes
Strongly Abelian Varieties and the Hamiltonian Property
 Journal of Mathematics
"... In this paper we show that every locally finite strongly Abelian variety satisfies the Hamiltonian property. An algebra is Hamiltonian if every one of its subuniverses is a block of some congruence of the algebra. A counterexample is provided to show that not all strongly Abelian varieties are H ..."
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are Hamiltonian. 1 Introduction The class of strongly Abelian algebras was first defined by Ralph McKenzie in [6]. The significance of these algebras, especially in the role they play in the classification of finite algebras and locally finite varieties was demonstrated in [6, 4, 9]. Much of the work
Three Remarks on the Modular Commutator
, 1996
"... . First a problem of Ralph McKenzie is answered by proving that in a finitely directly representable variety every directly indecomposable algebra must be finite. Then we show that there is no local proof of the fundamental theorem of Abelian algebras nor of H. P. Gumm's permutability result ..."
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. First a problem of Ralph McKenzie is answered by proving that in a finitely directly representable variety every directly indecomposable algebra must be finite. Then we show that there is no local proof of the fundamental theorem of Abelian algebras nor of H. P. Gumm's permutability
On Jonsson's theorem
, 1984
"... This paper surveys some results which are closely related to J6nsson's famous theorem. The theorem states that every subdirectly irreducible algebra in the variety generated by a class ~l of similar algebras is in HSPu (~f) provided V(Y() is distributive (i.e. has distributive congruence lattic ..."
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applications of J6nsson's theorem. Kirby Baker has shown that a finite algebra in a distributive variety has a finite basis for its equational theory [1]. Ralph McKenzie has given several applications to lattice varieties and lattice structure theory in [19]. The first section of this paper shows how J6
An Easy Way To Minimal Algebras
"... A finite algebra C is called minimal with respect to a pair δ < θ of its congruences if every unary polynomial f of C is either a permutation, or f(θ) ⊆ δ. It is the basic idea of tame congruence theory developed by Ralph McKenzie and David Hobby [7] to describe finite algebras via minimal algeb ..."
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A finite algebra C is called minimal with respect to a pair δ < θ of its congruences if every unary polynomial f of C is either a permutation, or f(θ) ⊆ δ. It is the basic idea of tame congruence theory developed by Ralph McKenzie and David Hobby [7] to describe finite algebras via minimal
ON GROUPS OF LARGE EXPONENTS N AND NPERIODIC PRODUCTS By
, 2005
"... I am indebted to my doctoral advisor Alexander Olshanskiy for many years of guidance, advice and encouragement. It has been a privilege to have been introduced to Combinatorial Group Theory by him and I have benefitted immensely from his enthusiasm and mathematical insight. I owe a great deal to my ..."
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to my professors at Moscow State University, especially to Alfred Shmelkin, who had a great influence on my mathematical forming. I wish to express my gratitude to Mark Sapir for many interesting courses he taught and numerous fruitful discussions we had. It is a pleasure to thank Ralph McKenzie
How to improve Bayesian reasoning without instruction: Frequency formats
 Psychological Review
, 1995
"... Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one s ..."
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Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50 % of all inferences by Bayesian algorithms. NonBayesian algorithms included simple versions of Fisherian and NeymanPearsonian inference. Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, equated probability theory with the common sense of educated people, who were known then as “hommes éclairés.” Laplace (1814/1951) declared that “the theory of probability is at bottom nothing more than good sense reduced to a calculus which evaluates that which good minds know by a sort of instinct,
Nashville, Tennessee Approved by:
, 2004
"... Dedicated to my wife, Regina, with my everlasting love. ii ACKNOWLEDGMENTS I would like to express my gratitude to a number of people without whose support this thesis would not have been possible. I could not possibly mention all of them. First and foremost I would like to thank my advisor, Profess ..."
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, Professor Ralph McKenzie. I would like to thank him for all the seminars I had the privilege to attend, for directing my first steps in Universal Algebra, for his patience in correcting my mistakes, for the countless hours of discussions and the work he put into my education. Ralph’s dedication to his
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