Solving Linear Equations over Polynomial Semirings
نویسنده
چکیده
We consider the problem of solving linear equations over various semirings. In particular, solving of linear equations over polynomial rings with the additional restriction that the solutions must have only non-negative coefficients is shown to be undecidable. Applications to undecidability proofs of several unification problems are illustrated, one of which, unification modulo one associative-commutative function and one endomorphism, has been a long-standing open problem. The problem of solving multiset constraints is also shown to be undecidable.
منابع مشابه
Solving Linear Systems on Linear Processor Arrays Using a ∗-Semiring Based Algorithm
∗-semirings are algebraic structures that provide a unified approach to solve several problem classes in computer science and operations research. Matrix computations over ∗-semirings are interesting because of their potential applications to linear algebra. In this paper, we present a parallel algorithm for solving systems of linear equations on ∗-semirings using linear arrays. Most of the wor...
متن کاملA Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases
In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...
متن کاملUniversal algorithms for solving the matrix Bellman equations over semirings
This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software implementations are discussed.
متن کاملExpansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind
In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is car...
متن کاملSolving Polynomial Systems on Semirings: A Generalization of Newton’s Method
Systems of polynomials on semirings arise in several branches of computer science, like static analysis of procedural programs or formal language theory. We propose a new technique for calculating the least fixed points of such polynomial systems. This technique is a generalization of Newton’s method, the well-known method for approximating a zero of a nonlinear function on the reals. We show t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996