Symbolic Algebraic Methods and Verification Methods

Symbolic-Algebraic Computations in Modeling Language for Mathematical Programming

Solution of Systems of Polynomial Equation by Using Bernstein Expansion

Symbolic Computation and Program Verification. Proving Partial Correctness and Synthesizing Optimal Algorithms∗

We present methods for checking the partial correctness of, respectively to optimize, imperativeprograms, using polynomial algebra methods, namely resultant computation and quantifier elimina-tion (QE) by cylindrical algebraic decomposition (CAD). The results are very promising but alsoshow that there is room for improvement of algebraic algorithms.

A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure

CIESIELSKI, KALLA, ZENG: TAYLOR EXPANSIONDIAGRAMS: A COMPACT CANONICAL REPRESENTATIONFOR ARITHMETIC EXPRESSIONS 1 Taylor Expansion Diagrams: A Compact Canonical Representation for Arithmetic Expressions

This paper presents a new, compact, canonical representation for arithmetic expressions, called Taylor Expansion Diagram. It can be used to facilitate the verification of RTL specifications and hardware implementations of arithmetic designs, and specifically the equivalence checking of complex algebraic and arithmetic expressions that arise in symbolic verification. This new representation is b...