A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Quantum automata and algebraic groups

2005
*
Journal of symbolic computation
*

We show that several problems which are known to be undecidable for probabilistic

doi:10.1016/j.jsc.2004.11.008
fatcat:5gdqdl25vrdaxabg37r5nxewl4
*automata*become decidable for*quantum*finite*automata*. ... Our main tool is an*algebraic*result of independent interest: we give an algorithm which, given a finite number of invertible matrices, computes the Zariski closure of the*group*generated by these matrices ... Acknowledgments P.K. would like to thank Etienne Ghys for pointing out Onishchik*and*Vinberg (1990) . The main algorithm was inspired by discussions with Joris van der Hoeven. ...##
###
Remarks on the structure of Clifford quantum cellular automata
[article]

2008
*
arXiv
*
pre-print

Therefore Clifford

arXiv:0812.0714v1
fatcat:choo33d77vcj5px5khikpiua5i
*quantum*cellular*automata*are induced by symplectic cellular*automata*in phase space. ... We characterize these symplectic cellular*automata**and*find that all possible local rules must be, up to some global shift, reflection invariant with respect to the origin. ...*Quantum*cellular*automata*provide model for analyzing*quantum*computational processes*and**quantum*computational complexity. ...##
###
Decidable and undecidable problems about quantum automata
[article]

2003
*
arXiv
*
pre-print

This result is in contrast with the corresponding situation for probabilistic finite

arXiv:quant-ph/0304082v1
fatcat:ofivd7nigjfj5ng66fvtkf75ym
*automata*for which it is known that strict*and*non-strict thresholds both lead to undecidable problems. ... We study the following decision problem: is the language recognized by a*quantum*finite automaton empty or non-empty? ... For the proof we use the fact that any compact matrix*group*is*algebraic**and*the*group*we consider can be given an effective description. ...##
###
Page 7608 of Mathematical Reviews Vol. , Issue 2002J
[page]

2002
*
Mathematical Reviews
*

(

*quantum*)*automata*. ... 2002):8 1005 81 is centred around the so-called history*group*(the analogue of the Heisenberg-Weyl*group*in the present framework)*and*its repre- sentations. ...##
###
Algebraic Characterization of the Class of Languages recognized by Measure Only Quantum Automata
[article]

2012
*
arXiv
*
pre-print

We study a model of one-way

arXiv:1206.1702v2
fatcat:nzq3ppcprrc6zhqvlomdh3cmwu
*quantum*automaton where only measurement operations are allowed (MOn-1qfa). ... We give an*algebraic*characterization of LMO, showing that the syntactic monoids of the languages in LMO are exactly the literal pseudovariety of J-trivial literally idempotent monoids, where J is the ... This class of*automata*has been fully characterized*algebraically*in [1] as the class of*automata*recognizing exactly regular languages having syntactic monoids in the class BG of block*groups*. ...##
###
Hybrid systems and quantum automata: Preliminary announcement
[chapter]

1995
*
Lecture Notes in Computer Science
*

Finite

doi:10.1007/3-540-60472-3_10
fatcat:lx3z7zidwjfvddiknyw7khpvtu
*automata**and*input-output systems are concerned with commutative R, while*quantum*systems, such as*quantum**automata*, are concerned with non-commutative R arising from Hermitian operators on the ... In this paper, we present a number of examples of hybrid systems*and**quantum**automata**and*point out some relationships between them. ...*Quantum**automata**and*languages*Algebra*of input events. Consider a language defined over an input alphabet Ω. ...##
###
Page 150 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

Mo- tivated by these observations, the authors formulate a class of cellular

*automata*directly in terms of crystals of irreducible finite- dimensional representations of*quantum*affine*algebras*U'(g,*and*... After recalling some facts about*quantum**groups*, it is shown that the problem of constructing a U;(g)-invariant quantization ; equivalent to the problem of constructing a U(g)-invariant*and*U(g){[A]) ...##
###
Page 2900 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
*
Mathematical Reviews
*

Since this

*algebra*underlies the noncompact*group*SU(1,1), we are thus able to define unambiguously the dynamical*group*related to the generalized*quantum*oscillator. ... )*Group*-theoretical approach to the classical*and**quantum*oscillator with time-dependent mass*and*frequency. ...##
###
Page 2366 of Mathematical Reviews Vol. , Issue 93d
[page]

1993
*
Mathematical Reviews
*

*Groups*Random Surfaces

*and*2D

*Quantum*Gravity ... ... on General Topology

*and*Applications Topology Symposium, Tsukuba Progress in Mathematics, 97 Providence, RI, 1988 Pushchino, 1990

*Quantum*

*groups*

*Quantum*logics, Part 1

*Quantum*logics, Part 2

*Quantum*mechanics ...

##
###
Decidable and Undecidable Problems about Quantum Automata

2005
*
SIAM journal on computing (Print)
*

This result is in contrast with the corresponding situation for probabilistic finite

doi:10.1137/s0097539703425861
fatcat:yy7c734d3rhczm2zvgse7ytcdy
*automata*, for which it is known that strict*and*nonstrict thresholds both lead to undecidable problems. ... We study the following decision problem: is the language recognized by a*quantum*finite automaton empty or nonempty? ... For the proof we use the fact that any compact matrix*group*is*algebraic*,*and*the*group*we consider can be given an effective description. Complex versus real entries. ...##
###
Index Theory of One Dimensional Quantum Walks and Cellular Automata

2012
*
Communications in Mathematical Physics
*

In the case of

doi:10.1007/s00220-012-1423-1
fatcat:crdsr5posfamrbkqpmjnidpemi
*quantum*walks, the index is integer-valued, whereas for cellular*automata*, it takes values in the*group*of positive rationals. ... For two types of such systems - namely*quantum*walks*and*cellular*automata*- we make this intuition precise by defining an index, a quantity that measures the "net flow of*quantum*information" through ... We gratefully acknowledge the support of the DFG (Forschergruppe 635)*and*the EU (projects CORNER*and*QUICS), as well as the Erwin Schrödinger Institute. ...##
###
Page 4933 of Mathematical Reviews Vol. , Issue 94h
[page]

1994
*
Mathematical Reviews
*

of

*algebras**and*their representations Quasicrystals: the state of the art Ramat-Gan, 1991/1992 Recent advances in real*algebraic*geometry*and*quadratic Rehovot, 1991/1992 Representation theory of*groups*... .. * 86002 Computational Crystal Growers, Geometry Center*Quantum*Deformations of*Algebras**and*their Representations Rough Sets—State of the Art*and*Perspectives, Ist International ...##
###
Page 3510 of Mathematical Reviews Vol. , Issue 93f
[page]

1993
*
Mathematical Reviews
*

methods in

*quantum*field theories .... * 81007 Tree*automata**and*languages * 68007 Trees*and*hierarchical structures * 92004 Trieste, 1990 * 81007 Turbulence*and*stochastic processes: Kolmogorov’s ideas ... Models Representation Theory of Lie*Groups**and*its Applications, 3rd ED isis ivcvcssdpiowndscvccrvvedscs ; Tree Languages*and*Tree*Automata*Yokohama, 1992 ...##
###
Book Review: Grundzüge der universellen Algebra

1978
*
Bulletin of the American Mathematical Society
*

In recent years probabilistic techniques have played a large role in constructive

doi:10.1090/s0002-9904-1978-14434-6
fatcat:ybgcqovj7rfdje3wgecdngjbxy
*quantum*field theory, but the random fields have been constructed on Euclidean space, rather than Minkowski space,*and*... the results for*quantum*fields have been obtained by analytic continuation. ... A third chapter lists examples: groupoids,*groups*, rings, lattices*and*Boolean*algebras*. ...##
###
Page 8742 of Mathematical Reviews Vol. , Issue 2003k
[page]

2003
*
Mathematical Reviews
*

By means of the crystal base theory, we study a class of such

*automata*associated with the*quantum*affine*algebra*U,(g,,) for the nonexceptional series g, = Pd we .C}"’, Dh’*and*p.. ... (RS-MURE; Moscow) Unitary representations of the*quantum*Lorentz*group*,*and*the*quantum*relativistic Toda chain. (Russian. Russian summary) Teoret. Mat. ...
« Previous

*Showing results 1 — 15 out of 5,033 results*