Quantum automata and algebraic groups

Authors:
Harm Derksen;Emmanuel Jeandel;Pascal Koiran
Affiliations:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States;Laboratoire de lInformatique du Parallélisme, Ecole Normale Supérieure de Lyon, 69364, France;Laboratoire de lInformatique du Parallélisme, Ecole Normale Supérieure de Lyon, 69364, France
Venue:
Journal of Symbolic Computation
Year:
2005

Citing 13
Cited 7

On the computational complexity and geometry of the first-order theory of the reals. Part III: quantifier elimination

Journal of Symbolic Computation
Deciding finiteness of matrix groups in deterministic polynomial time

ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
On the combinatorial and algebraic complexity of quantifier elimination

Journal of the ACM (JACM)
An algorithm for computing the integral closure

Journal of Symbolic Computation
Quantum automata and quantum grammars

Theoretical Computer Science
Analogies and differences between quantum and stochastic automata

Theoretical Computer Science
Computing the Radical of an Ideal in Positive Characteristic

Journal of Symbolic Computation
The calculation of radical ideals in positive characteristic

Journal of Symbolic Computation
Derivations and radicals of polynomial ideals over fields of arbitrary characteristic

Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Some Recursive Unsolvable Problems Relating to Isolated Cutpoints in Probabilistic Automata

Proceedings of the Fourth Colloquium on Automata, Languages and Programming
The Solution of Problems Relative to Probabilistic Automata in the Frame of the Formal Languages Theory

GI - 4. Jahrestagung
On the power of quantum finite state automata

FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Decidable and Undecidable Problems about Quantum Automata

SIAM Journal on Computing

Some formal tools for analyzing quantum automata

Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Around the numeric-symbolic computation of differential Galois groups

Journal of Symbolic Computation
Improved Undecidability Results on the Emptiness Problem of Probabilistic and Quantum Cut-Point Languages

SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Constructing algebraic groups from their Lie algebras

Journal of Symbolic Computation
Uncomputability below the real halting problem

CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Real computational universality: the word problem for a class of groups with infinite presentation

MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Numeric-symbolic methods for computing the Liouvillian solutions of differential equations and systems

ACM Communications in Computer Algebra

Quantified Score

Hi-index	0.00

Visualization

Abstract

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