Formal methods are a suite of mathematically grounded techniques that underpin the design, specification, and verification of programming languages and software systems.

In the first part of this paper, the concept of logical reduction is presented. Minimal preferred variable inequalities are introduced, and algorithms are given for their calculation. A simple ...

For a stochastic programming problem with a nonsmooth objective a recursive stochastic subgradient method is proposed in which successive directions are obtained from quadratic programming subproblems ...

Formal methods offer a mathematically rigorous framework for the specification, development and verification of programming languages and software systems.