scholarly journals Improved algorithms for computing the greatest right and left invariant Boolean matrices and their application

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2809-2831
Author(s):  
Stefan Stanimirovic ◽  
Aleksandar Stamenkovic ◽  
Miroslav Ciric
Keyword(s):  
Computational Linguistics ◽  
Zero Divisor ◽  
Matrix Equations ◽  
Weighted Automata ◽  
Idempotent Semirings ◽  
Quasi Order ◽  
Invariant Matrices ◽  
Partition Refinement

We define right and left invariant matrices as Boolean matrices that are solutions to certain systems of matrix equations and inequalities over additively idempotent semirings. We provide improved algorithms for computing the greatest right and left invariant equivalence and quasi-order matrices. The improvements are based on the usage of the well-known partition refinement technique. Afterwards, we present the application of right invariant matrices in the determinization of weighted automata over additively idempotent, commutative and zero-divisor free semirings. In particular, we provide improvements of the well-known determinization method of weighted automata over tropical semirings given by Mohri [Computational Linguistics 23 (2) (1997) 269-311].

Solution of a Linear Nondegenerate Matrix Equation Based on the Zero Divisor

2021 ◽  
pp. 49-59
Author(s):  
N.E. Zubov ◽  
V.N. Ryabchenko
Keyword(s):  
Power Systems ◽  
Matrix Equation ◽  
Zero Divisor ◽  
Iterative Solvers ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Proved Theorem ◽  
Nondegenerate Matrix ◽  
The Matrix ◽  
The Right

New formulas were obtained to solve the linear non-degenerate matrix equations based on zero divisors of numerical matrices. Two theorems were formulated, and a proof to one of them is provided. It is noted that the proof of the second theorem is similar to the proof of the first one. The proved theorem substantiates new formula in solving the equation equivalent in the sense of the solution uniqueness to the known formulas. Its fundamental difference lies in the following: any explicit matrix inversion or determinant calculation is missing; solution is "based" not on the left, but on the right side of the matrix equation; zero divisor method is used (it was never used in classical formulas for solving a matrix equation); zero divisor calculation is reduced to simple operations of permutating the vector elements on the right-hand side of the matrix equation. Examples are provided of applying the proposed method for solving a nondegenerate matrix equation to the numerical matrix equations. High accuracy of the proposed formulas for solving the matrix equations is demonstrated in comparison with standard solvers used in the MATLAB environment. Similar problems arise in the synthesis of fast and ultrafast iterative solvers of linear matrix equations, as well as in nonparametric identification of abnormal (emergency) modes in complex technical systems, for example, in the power systems

Catch a Liar by the Tale: Computational Linguistics and Classifying Deception

2006 ◽  
Author(s):  
Wendy E. Chan ◽  
David M. Arney ◽  
Josh Morgan ◽  
Lauren Stevenson ◽  
Kevin Reimer ◽  
...  
Keyword(s):  
Computational Linguistics
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