Prime Decomposition Problem for Several Kinds of Regular Codes

RESTRICTED SETS OF TRAJECTORIES AND DECIDABILITY OF SHUFFLE DECOMPOSITIONS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054105003364 ◽

2005 ◽

Vol 16 (05) ◽

pp. 897-912 ◽

Cited By ~ 3

Author(s):

MICHAEL DOMARATZKI ◽

KAI SALOMAA

Keyword(s):

Regular Languages ◽

Decomposition Problem ◽

Open Question ◽

Free Set ◽

Context Free ◽

Undecidability Result

The decidability of the shuffle decomposition problem for regular languages is a long standing open question. We consider decompositions of regular languages with respect to shuffle along a regular set of trajectories and obtain positive decidability results for restricted classes of trajectories. Also we consider decompositions of unary regular languages. Finally, we establish in the spirit of the Dassow-Hinz undecidability result an undecidability result for regular languages shuffled along a fixed linear context-free set of trajectories.

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Zhang Neural Network Model for Solving LQ Decomposition Problem of Dynamic Matrix With Application to Mobile Object Localization

10.1109/ijcnn52387.2021.9533326 ◽

2021 ◽

Author(s):

Jinjin Guo ◽

Binbin Qiu ◽

Min Yang ◽

Yunong Zhang

Keyword(s):

Neural Network ◽

Network Model ◽

Neural Network Model ◽

Object Localization ◽

Mobile Object ◽

Decomposition Problem ◽

Dynamic Matrix ◽

Zhang Neural Network

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Constructing Gröbner bases for Noetherian rings

Mathematical Structures in Computer Science ◽

10.1017/s0960129513000509 ◽

2013 ◽

Vol 24 (2) ◽

Cited By ~ 4

Author(s):

HERVÉ PERDRY ◽

PETER SCHUSTER

Keyword(s):

Gröbner Basis ◽

Finite Depth ◽

Commutative Rings ◽

Polynomial Ideal ◽

Constructive Proof ◽

Noetherian Rings ◽

Grobner Basis ◽

Finitely Generated ◽

Prime Decomposition ◽

Separate Paper

We give a constructive proof showing that every finitely generated polynomial ideal has a Gröbner basis, provided the ring of coefficients is Noetherian in the sense of Richman and Seidenberg. That is, we give a constructive termination proof for a variant of the well-known algorithm for computing the Gröbner basis. In combination with a purely order-theoretic result we have proved in a separate paper, this yields a unified constructive proof of the Hilbert basis theorem for all Noether classes: if a ring belongs to a Noether class, then so does the polynomial ring. Our proof can be seen as a constructive reworking of one of the classical proofs, in the spirit of the partial realisation of Hilbert's programme in algebra put forward by Coquand and Lombardi. The rings under consideration need not be commutative, but are assumed to be coherent and strongly discrete: that is, they admit a membership test for every finitely generated ideal. As a complement to the proof, we provide a prime decomposition for commutative rings possessing the finite-depth property.

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