Abstract Numerical and symbolic methods for optimization are used extensively in engineering, industry, finance. Various to reduce problems of interest ones that amenable solution by these methods. We develop a framework designing applying such reductions, using the Lean programming language interactive proof assistant. Formal verification makes process more reliable, availability an ambient ma...

This paper explores the algebraic matching approach for detection of vulnerabilities in binary codes. The algebraic programming system is used for implementing this method. It is anticipated that models of vulnerabilities and programs to be verified are presented as behavior algebra and action language specifications. The methods of algebraic matching are based on rewriting rules and techniques...

Calculational proofs—proofs by stepwise formula manipulation—are praised for their rigor, readability, and elegance. It seems desirable to reuse this style, often employed on paper, in the context of mechanized reasoning, and in particular, program verification. This work leverages the power of SMT solvers to machine-check calculational proofs at the level of detail they are usually written by ...

The forward position kinematics (FPK) of a parallel manipulator with new architecture supposed to be used as a moving mechanism in a flight simulator project is discussed in this paper. The closed form solution for the FPK problem of the manipulator is first determined. It has, then, been shown that there are at most 24 solutions for FPK problem. This result has been verified by using other tec...

In this paper, the propagation of electromagnetic waves through an infinite slab of uni- or bi- axial chiral medium is analytically formulated for an arbitrary incidence using 4×4 matrix method. In this powerful method, a state vector differential equation is extracted whose solution is given in terms of a transition matrix relating the tangential components of electric and magnetic fields at t...