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Correction to "complexity of ideals in finite semigroups and finite-state machines"

Kenneth Krohn, Richard Mateosian, John Rhodes
1967 Mathematical Systems Theory  
In the displayed formula defining h2 on page 63 replace "if z = d or z = e or x = 0" by "if z = d or x = 0", and also replace "if z = u and x = (a, b)" by "otherwise".  ...  In the displayed formula defining hi on page 63 replace "u" by "c" everywhere to the right o f the bracket.  ...  In the last line o f Proposition 2 o f Section 3, p. 65, replace "and Vt an ideal o f Vi+~' by "and Via subideal of Vi+~".  ... 
doi:10.1007/bf01695170 fatcat:fxlulbzqzjfhvnr5gnyaf42fou

Page 1341 of Mathematical Reviews Vol. 34, Issue 5 [page]

1967 Mathematical Reviews  
semigroups and finite-state machines.  ...  The least number of group blocks required in any decomposition of a machine M isthe complexity number #¢(M) ; it depends only on the machine semigroup, and not on any state representation used.  ... 

Cumulative subject index

1990 Information and Computation  
Algebras and first-order logic for complexity class NC, 87, 241 process, associated priorities, 87, 58 Algorithms Arimoto-Blahut, in calculating capacity of continuous-input discrete-output memoryless  ...  207 Automata finite, nondeterminism in, measurement, 86, 179 nonuniform, over groups, 89, 109 B Bisimulation in behavioral preorders, and divergence in communicating systems, analysis, 85, 202 ' Boldface  ...  complexity, 86, 107 Processes finite state, and CCS expressions and problems of equivalence, 86, 43 Programs O-branching, polynomial size, computa-Stability and computability, in coherent domains, 86,  ... 
doi:10.1016/0890-5401(90)90012-7 fatcat:abh2kjcxfveulfizk3aa5ifc64

Some Complexity Results for Polynomial Ideals

Ernst W. Mayr
1997 Journal of Complexity  
We discuss further complexity results for problems related to polynomial ideals, like the word and subword problems for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz in a  ...  In this paper, we survey some of our new results on the complexity of a number of problems related to polynomial ideals.  ...  We state complexity bounds as worst-case bounds in terms of the input size, which is the number of bits used to encode the input.  ... 
doi:10.1006/jcom.1997.0447 fatcat:d3cz6pfw3za4disutcnitfvlsa

Lower bounds for complexity of finite semigroups

John Rhodes, Bret R. Tilson
1971 Journal of Pure and Applied Algebra  
We assume the reader is familiar with the definition and elementary properties Of the {group) complexity of a finite semigroup or of a fiiite statt sequential mactrine.  ...  In all examples and ems known to the authors #F&S) = +(S) and we conjecture (with sume hope) 4+,&Y') = 4$-(S) fur ail finite semigroups S.  ...  Complexity of inverse semigroups In the folklwing ail semigraups arp assumed to have finite order.  ... 
doi:10.1016/0022-4049(71)90012-0 fatcat:7y2mvbxsu5co3ete3hl5wrb5sa

The complexity of the word problems for commutative semigroups and polynomial ideals

Ernst W Mayr, Albert R Meyer
1982 Advances in Mathematics  
Any decision procedure for the word problems for commutative semigroups and polynomial deals inherently requires computational storage space growing exponentially with the size of the problem instance  ...  This bound is achieved by a simple procedure for the semigroup problem.  ...  Formally, a 3-counter machine C consists of a finite set Q of states, a pair of distinguished states q0 and q, E Q (where q0 is called the initial and q, the accepfing state), and a (transition) function  ... 
doi:10.1016/0001-8708(82)90048-2 fatcat:xg2x3ubsfncs5e4fj4uhppugey

Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels [article]

Vishesh Karwa, Debdeep Pati, Sonja Petrović, Liam Solus, Nikita Alexeev, Mateja Raič, Dane Wilburne, Robert Williams, Bowei Yan
2021 arXiv   pre-print
The question of model goodness of fit, a first step in data analysis, is easy to state, but often difficult to implement in practice, particularly for large and sparse or small-sample but structured data  ...  Specifically, we construct finite-sample tests for three different variants of the stochastic blockmodel (SBM).  ...  To do this, we identify a finite collection of binomials generating the toric ideal associated to the ER-SBM.  ... 
arXiv:1612.06040v2 fatcat:fvyuc6jppfaqnokfftbn3yxvwi

The q-theory of finite semigroups: history and mathematics [article]

Stuart W. Margolis
2014 arXiv   pre-print
This paper is a historical and mathematical review of the book, "The q-theory of Finite Semigroups" by John Rhodes and Benjamin Steinberg.  ...  Conversely, any wreath product decomposition of finite semigroups has a corresponding interpretation in terms of factorizations of finite state machines.  ...  It determined the structure of the minimal ideal of a finite semigroup and in modern terminology, the structure of finite completely simple semigroups.  ... 
arXiv:1409.2308v2 fatcat:f6awhe4vjbg5jmxobgrtj3sifi

Transformation Semigroups as Constructive Dynamical Spaces [chapter]

Attila Egri-Nagy, Paolo Dini, Chrystopher L. Nehaniv, Maria J. Schilstra
2010 Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering  
After explaining how semigroups can be seen as constructive dynamical spaces we show how John Rhodes's formalism can be used to define an Interaction Machine and provide a conceptual discussion of its  ...  We close the paper with preliminary results from the holonomy decomposition of the semigroups associated with two automata derived from the same p53-mdm2 regulatory pathway being investigated in other  ...  Acknowledgments Partial support for this work by the OPAALS (FP6-034824) and the BIONETS (FP6-027748) EU projects is gratefully acknowledged.  ... 
doi:10.1007/978-3-642-14859-0_19 fatcat:hkzuxmjzb5f6zcuwvsva27fmle

Data Flow Algorithms for Processors with Vector Extensions

Lee Barford, Shuvra S. Bhattacharyya, Yanzhou Liu
2015 Journal of Signal Processing Systems  
Two examples of applying this methodology are given: (1) infinite impulse response filters and (2) finite state machines.  ...  The correctness and performance of the resulting IIR filters and one class of FSMs are studied.  ...  Experimental Verification Finite State Machines References [4] and [5] present applications verifying the correctness and studies of the performance of the FSM method running on GPUs and on multicore  ... 
doi:10.1007/s11265-015-1045-x fatcat:sasmbadjbvbinel63egagtehxm

Computing rank of finite algebraic structures with limited nondeterminism [article]

Jeffrey Finkelstein
2020 arXiv   pre-print
In the case of groups, the previous best algorithm for computing rank used polylogarithmic space. We reduce the best upper bounds on the complexity of computing rank for groups and for quasigroups.  ...  Furthermore, if the quasigroup is a group, then the problem is also decidable by a Turing machine using O(log n) space and O(log^2 n) bits of nondeterminism with the ability to read the nondeterministic  ...  The machine M 1 accepts if and only if each of the simulations of M 2 accepts. The correctness of M 1 follows from the correctness of f and M 2 . The only remaining issue is the complexity of M 1 .  ... 
arXiv:1406.0879v4 fatcat:pmnljr6a2rgitgs6lmffvtcc2u

Page 300 of Mathematical Reviews Vol. 45, Issue 1 [page]

1973 Mathematical Reviews  
- tion, correctness of states and inputs, etc.  ...  Theorem 2 implies the non-existence of universal Turing machines with 3 | states and 2 symbols. A. Adém (Budapest) Levin, V.  ... 

Page 744 of Mathematical Reviews Vol. 38, Issue 4 [page]

1969 Mathematical Reviews  
Author’s summary : “A standard method for finite autom- aton state assignment is considered, in which the mini- mal disjunctive normal forms of the excitation functions and the outputs are obtained in  ...  The author studies the behavior of a self-correcting system while it is in the process of making corrections, and the behavior of a certain probabilistic automaton.  ... 

Subject index volumes 1–200

1999 Theoretical Computer Science  
machines, behavior of -, 2033 finite state machine, 233 finite state machines, 859 decomposability of nets into -, 579 products of -, 3070 finite state pattern matching machines, 497 transduction  ...  recursively enumerable sets, 6 FINITEREVERSAL, class of languages, 123 finite-state automata, 2107, 2134, 2557 Rabin-Scott -, 2557 finite-state defense, 1262 machine, 355 finite-state machines  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Remarks on algebraic decomposition of automata

A. R. Meyer, C. Thompson
1969 Mathematical Systems Theory  
A version of the Krohn-Rhodes decomposition theorem for finite automata is proved in which capabilities as well as semigroups are preserved.  ...  Another elementary proof of the usual Krohn-Rhodes theorem is also presented.  ...  A A semiautomaton (or state machine) A consists of a finite set Q (of A states)., a finite set 2 (of inputs) a and a set of (transition) functions A A A A A from Q into Q indexed by £ .  ... 
doi:10.1007/bf01746516 fatcat:4exq3zxarvdsxmhwq3eikmyna4
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