Chun-Ming Yuan

A characteristic set method for solving boolean equations and applications in cryptanalysis of stream ciphers

This paper presents a characteristic set method for solving Boolean equations, which is more efficient and has better properties than the general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.

Submersive rational difference systems and their accessibility

The paper describes an algebraic construction of the inversive difference field associated with a discrete-time rational nonlinear control system under the assumption that the system is submersive. We prove that a system is submersive iff its associated difference ideal is proper, prime and reflexive. Next, we show that Kähler differentials of the above inversive field define a module over the corresponding ring of Ore operators, and relate its torsion submodule to the vector space of autonomous one-forms, introduced elsewhere. The above results allow us to check accessibility property and simplify transfer functions with computer algebra techniques.

Curve fitting and optimal interpolation on CNC machines based on quadratic B-splines

In this paper, curve fitting of 3-D points generated by G01 codes and interpolation based on quadratic B-splines are studied. Feature points of G01 codes are selected using an adaptive method. Next, quadratic B-splines are obtained as the fitting curve by interpolating these feature points. Computations required in implementing the velocity planning algorithm mentioned by Timer et al. are very complicated because of the appearance of high-order curves. An improved time-optimal method for the quadratic B-spline curves is presented to circumvent this issue. The algorithms are verified with simulations as well as on real CNC machines.

Intersection theory in differential algebraic geometry: Generic intersections and the differential Chow form

In this paper, an intersection theory for generic differential polynomials is presented. The intersection of an irreducible differential variety of dimension

Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error

d

A characteristic set method for ordinary difference polynomial systems

and order

Characteristic set method for differential-difference polynomial systems

h

Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines

with a generic differential hypersurface of order

Sparse differential resultant

s

Certified approximation of parametric space curves with cubic B-spline curves

is shown to be an irreducible variety of dimension