Testing Equalities of Multiplicative Representations in Polynomial Time (Extended Abstract)
نویسنده
چکیده
k For multiplicative representations ni=, ay' and n;=, Byi , where ai, pj are non-zero elements of some algebraic number field K and ni, mj are rational integers, we present a deterministic polynomial time algorithm that decides whether HfZl ay' equals l$=, py'. The running time of the algorithm is polynomial in the number of bits required to represent the number field K, the elements a i , p j and the integers ni, mj.
منابع مشابه
A Unified Approach for Design of Lp Polynomial Algorithms
By summarizing Khachiyan's algorithm and Karmarkar's algorithm forlinear program (LP) a unified methodology for the design of polynomial-time algorithms for LP is presented in this paper. A key concept is the so-called extended binary search (EBS) algorithm introduced by the author. It is used as a unified model to analyze the complexities of the existing modem LP algorithms and possibly, help ...
متن کاملEEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations
GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...
متن کاملOrienting Equalities with the Knuth-Bendix Order
Orientability of systems of equalities is the following problem: given a system of equalities s1 ≃ t1, . . . , sn ≃ tn, does there exist a simplification ordering ≻ which orients the system, that is for every i ∈ {1, ..., n}, either si ≻ ti or ti ≻ si. This problem can be used in rewriting for finding a canonical rewrite system for a system of equalities and in theorem proving for adjusting sim...
متن کاملInter-procedural Two-Variable Herbrand Equalities
We prove that all valid Herbrand equalities can be interprocedurally inferred for programs where all assignments are taken into account whose right-hand sides depend on at most one variable. The analysis is based on procedure summaries representing the weakest preconditions for finitely many generic post-conditions with template variables. In order to arrive at effective representations for all...
متن کاملA method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra
In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonst...
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 1993