John Rhodes

Q: What Schools Are Affiliated With John Rhodes

John Rhodes is affiliated with the following schools: University of California, Berkeley, Massachusetts Institute of Technology

John Rhodes 's AcademicInfluence.com Rankings

John Rhodes

Mathematics

#5045

World Rank

#7134

Historical Rank

#1685

USA Rank

Measure Theory

#2935

World Rank

#3484

Historical Rank

#848

USA Rank

mathematics Degrees

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Mathematics

Why Is John Rhodes Influential?

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According to Wikipedia, John Lewis Rhodes is a mathematician known for work in the theory of semigroups, finite state automata, and algebraic approaches to differential equations. Education and career Rhodes was born in Columbus, Ohio, on July 16, 1937, but grew up in Wooster, Ohio, where he founded the Wooster Rocket Society as a teenager. In the fall of 1955, Rhodes entered the Massachusetts Institute of Technology intending to major in physics, but he soon switched to mathematics, earning his B.S. in 1960 and his Ph.D. in 1962. His Ph.D. thesis, co-written with a graduate student from Harvard, Kenneth Krohn, became known as the Prime Decomposition Theorem, or more simply the Krohn–Rhodes Theorem. After a year on an NSF fellowship in Paris, France, he became a member of the Faculty of Mathematics at the University of California, Berkeley, where he spent his entire teaching career.

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John Rhodes 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The q-theory of Finite Semigroups (2008) (359)
Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines (1965) (316)
Ash's Type II Theorem, Profinite Topology and Malcev Products: Part I (1991) (121)
Almost finite expansions of arbitrary semigroups (1984) (102)
The kernel of monoid morphisms (1989) (89)
Undecidability of the identity problem for finite semigroups (1992) (76)
Improved lower bounds for the complexity of finite semigroups (1972) (56)
A property of finite simple non-abelian groups (1965) (55)
The Evolution and Understanding of Hierarchical Complexity in Biology from an Algebraic Perspective (1999) (52)
Undecidability, Automata, and Pseudovarities of Finite Semigroups (1999) (49)
Complexity of Finite Semigroups (1968) (49)
Group Theory via Global Semigroup Theory (1989) (44)
Applications of Automata Theory and Algebra via the Mathematical Theory of Complexity to Biology (2009) (42)
Some results on finite semigroups (1966) (41)
Aperiodic Pointlikes and Beyond (2007) (40)
Algebraic Principles for the Analysis of a Biochemical System (1967) (38)
New Techniques in Global Semigroup Theory (1987) (38)
Lower bounds for complexity of finite semigroups (1971) (35)
Decomposition techniques for finite semigroups, using categories II (1989) (34)
Infinite iteration of matrix semigroups II. Structure theorem for arbitrary semigroups up to aperiodic morphism (1986) (32)
Profinite Semigroups, Varieties, Expansions and the Structure of Relatively Free Profinite Semigroups (2001) (29)
Decidability of complexity one-half for finite semigroups (1982) (28)
Maximal subsemigroups of finite semigroups (1968) (27)
The fundamental lemma of complexity for arbitrary finite semigroups (1968) (26)
Chapter 4. Synthesis of the Classical and Modern Theory of Finite Semigroups (1973) (25)
Kernel systems—A global study of homomorphisms on finite semigroups (1977) (24)
Semigroups whose idempotents form a subsemigroup (1990) (24)
Pointlike Sets, Hyperdecidability and the Identity Problem for Finite Semigroups (1999) (23)
Monoids Acting on Trees: Elliptic and wreath Products and the Holonomy Theorem for Arbitrary Monoids with Applications to Infinite Groups (1991) (22)
Closed subgroups of free profinite monoids are projective profinite groups (2006) (21)
The Complexity of Finite Semigroups (2009) (21)
Realizing Complex Boolean Functions with Simple Groups (1966) (20)
Characters and complexity of finite semigroups (1969) (20)
Finite Semigroups Whose Idempotents Commute or Form a Subsemigroup (1987) (19)
Representation Theory of Finite Semigroups over Semirings (2010) (19)
Methods of the Algebraic Theory of Machines. I: Decomposition Theorem for Generalized Machines; Properties Preserved under Series and Parallel Compositions of Machines (1967) (18)
Algebraic theory of finite semigroups (1970) (18)
Subsemigroups and complexity via the Presentation Lemma (1995) (18)
Proof of the Fundamental Lemma of Complexity (Strong Version) for Arbitrary Finite Semigroups (1974) (18)
Infinite Iteration of Matrix Semigroups I. Structure Theorem for Torsion Semigroups (1986) (17)
Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions (2015) (17)
Unified theory for finite Markov chains (2017) (17)
A Profinite Approach to Stable Pairs (2006) (17)
Automatic analysis of computation in biochemical reactions (2008) (16)
New Representations of Matroids and Generalizations (2011) (16)
Prime decomposition theorem for arbitrary semigroups: general holonomy decomposition and synthesis theorem (1988) (13)
C-independence and c-rank of posets and lattices (2011) (13)
BOOLEAN REPRESENTATIONS OF MATROIDS AND LATTICES (2011) (12)
Boolean Representations of Simplicial Complexes and Matroids (2015) (11)
Finite binary relations have no more complexity than finite functions (1974) (11)
A homomorphism theorem for finite semigroups (1967) (11)
RESULTS ON FINITE SEMIGROUPS DERIVED FROM THE ALGEBRAIC THEORY OF MACHINES. (1965) (11)
Geometric Semigroup Theory (2011) (10)
Local Complexity of Finite Semigroups (1976) (10)
Random walks on semaphore codes and delay de Bruijn semigroups (2015) (9)
Complexity Pseudovarieties Are not Local: Type Ii Subsemigroups Can Fall Arbitrarily in Complexity (2006) (9)
An effective lower bound for group complexity of finite semigroups and automata (2008) (9)
A reduction theorem for complexity of finite semigroups (1975) (8)
Reduction theorem for the Type-II conjecture for finite monoids (1990) (8)
Nets of Threshold Elements (1965) (8)
Join irreducible semigroups (2017) (7)
Chapter 2. Axioms for complexity for all finite semigroups (1973) (7)
Monoids and semigroups with applications : proceedings of the Berkeley Workshop in Monoids, Berkeley, 31 July-5 August 1989 (1991) (6)
Krohn-Rhodes complexity pseudovarieties are not finitely based (2005) (6)
Superboolean rank and the size of the largest triangular submatrix of a random matrix (2011) (6)
Join Irreducible Pseudovarieties, Group Mapping, and Kovács-Newman Semigroups (2004) (5)
Decidability and hyperdecidability of joins of pseudovarieties (1998) (5)
Complexity of grammars by group theoretic methods (1968) (5)
Further Results on Monoids Acting on Trees (2011) (4)
ALGEBRAIC THEORY OF MACHINES. I. THE MAIN DECOMPOSITION THEOREM. PRIME DECOMPOSITION THEOREM FOR FINITE SEMIGROUPS. (1963) (4)
Normal distributions of finite Markov chains (2019) (4)
On the subsemigroup complex of an aperiodic Brandt semigroup (2017) (4)
Algebraic and Topological Theory of Languages (1995) (4)
On the topology of a boolean representable simplicial complex (2015) (4)
A short proof that Ŝ+A is finite if S is finite (1988) (3)
Krohn-Rhodes theory, hierarchies & evolution (1996) (3)
Survey of Global Semigroup Theory (1990) (3)
Turing machines and bimachines (2008) (3)
On the cantor-dedekind property of the Tilson order on categories and graphs (1987) (3)
Computational complexity of generalized pattern matching (2000) (3)
Type-II conjecture is true for finite I-trivial monoids (1992) (3)
Transformations, Semigroups, and Metabolism (1968) (2)
Global structure theories for finite semigroups—Introduction (1973) (2)
Holonomy theorem for finite semigroups (2020) (2)
Book Review: The algebraic theory of semigroups (1970) (2)
On the atoms of algebraic lattices arising in 픮-theory (2016) (2)
Review: A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, and E. S. Ljapin, Semigroups, and László Rédei, The theory of finitely generated commutative semigroups, and Karl Heinrich Hofmann and Paul S. Mostert, Elements of compact semigroups (1970) (2)
The semaphore codes attached to a Turing machine via resets and their various limits (2016) (2)
On the Wilson monoid of a pairwise balanced design (2019) (2)
On the Dowling and Rhodes lattices and wreath products (2017) (2)
Matroids, hereditary collections and simplicial complexes having boolean representations (2012) (2)
A new notion of vertex independence and rank for finite graphs (2012) (2)
The relationship of Al Clifford's work to the current theory of semigroups (1996) (2)
Algebraic and Topological Theory of Languages and Computation, Part I: Theorems for Arbitrary Labguages Generalizing the Theorems of Eilenberg, Kleene, Schützenberger and Straubing (1984) (1)
Truncated boolean representable simplicial complexes (2019) (1)
The Equational Theory (2009) (1)
Complexity of ideals in finite semigroups and finite-state machines (1967) (1)
Bounds on mixing time of finite Markov chains. (2020) (1)
Degree 2 Transformation Semigroups as Continuous Maps on Graphs: Complexity and Examples (2023) (1)
The Triangular Product and Decomposition Results for Semirings (2009) (0)
Operations on Simplicial Complexes (2015) (0)
Paving Simplicial Complexes (2015) (0)
Finite semigroups, feedback, and the Letichevsky criteria on non-empty words in finite automata (2003) (0)
On the subsemigroup complex of an aperiodic Brandt semigroup (2018) (0)
Grand unified theory for Tsetlin libraries (2017) (0)
Foundations for Finite Semigroup Theory (2009) (0)
What is Finite Group Theory (2009) (0)
The kernel of a homomorphism on a finite semigroup (1974) (0)
On join irreducible $J$-trivial semigroups (2022) (0)
Markov Chains Through Semigroup Graph Expansions (A Survey) (2020) (0)
Two-Sided Complexity and the Complexity of Operators (2009) (0)
Degree 2 transformation semigroups as continuous maps on graphs: Foundations and structure (2020) (0)
The q-operator (2009) (0)
An algebraic analysis of Turing machines and Cook's Theorem leading to a profinite fractal dierential equation and a random walk on a deterministic Turing machine (2006) (0)
Posets and Lattices (2015) (0)
The Abstract Spectral Theory of PV (2009) (0)
Complexity of Finite State Machines as a Tool for Understanding Software Evolution (2007) (0)
Shellability and Homotopy Type (2015) (0)
The lattice of flats of a boolean representable simplicial complex (2015) (0)
Automata Models and the Complexity of Finite State Machines (2009) (0)
Algebraic Lattices, Continuous Lattices and Closure Operators (2009) (0)
Correction to “complexity of ideals in finite semigroups and finite-state machines” (1967) (0)
Global local covers (2019) (0)
Prologue: Birth, Death, Time, Space, Existence, Understanding, Science, and Religion [Outline] (2009) (0)
Towards Krohn-Rhodes complexity (2021) (0)
A Reformulation of Physics (2009) (0)
A Generalization of Finite Group Theory to Finite Semigroups (2009) (0)
In (l) Birget studied the expansion Si and proved that if S is a finite semigroup, then $2 is finite. The techniques introduced in the proof have wider applications A SHORT PROOF THAT $2 IS FINITE IF S IS FINITE (1988) (0)
Bret Tilson: his Life and Work (2010) (0)
Boolean and Superboolean Matrices (2015) (0)
ernel Systems-A Global Study o on Finite Semigw (1977) (0)

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What Schools Are Affiliated With John Rhodes ?

John Rhodes is affiliated with the following schools:

John Rhodes 's Academic­Influence.com Rankings