We present RFN, a formal property verification tool based on abstraction refinement. Abstraction refinement is a strategy for property verification. It iteratively refines an abstract model to better approximate the behavior of the original design in the hope that the abstract model alone will provide enough evidence to prove or disprove the property.

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We present algorithms for 3-D manipulation and conformational analysis of molecular chains, when bond lengths, bond angles and related dihedral angles remain fixed. These algorithms are useful for local deformations of linear molecules, exact ring closure in cyclic molecules and molecular embedding for short chains. Other possible applications include structure prediction, protein folding, conformation energy analysis and 3D molecular matching and docking. The algorithms are applicable to all serial molecular chains and make no assumptions about their geometry. We make use of results on direct and inverse kinematics from robotics and mechanics literature and show the correspondence between kinematics and conformational analysis of molecules. In particular, we pose these problems algebraically and compute all the solutions making use of the structure of these equations and matrix computations. The algorithms have been implemented and perform well in practice. In particular, they take tens of milliseconds on current workstations for local deformations and chain closures on molecular chains consisting of six or fewer rotatable dihedral angles.

We present fast and robust algorithms for the inverse kinematics of serial manipulators consisting of six or fewer joints. When stated mathematically, the problem of inverse kinematics reduces to simultaneously solving a system of algebraic equations. In this paper, we use a series of algebraic and numeric transformations to reduce the problem to computing the eigenstructure of a matrix pencil. To efficiently compute the eigenstructure, we make use of the symbolic formulation of the matrix and use a number of techniques from linear algebra and matrix computations. The resulting algorithm computes all the solution of a serial manipulator with six or fewer joints in the order of tens of milliseconds on the current workstations. It has been implemented as part of a generic package, KINEM, for the inverse kinematics of serial manipulators.>