Evidence Algorithm and Processing Formalized Mathematical Texts

The goal of a research programme Evidence Algorithm is a development of an open system of automated proving that is able to accumulate mathematical knowledge and to prove theorems in a context of a self-contained mathematical text. By now, the first version of such a system called a System for Automated Deduction, SAD, is implemented in software. The system SAD possesses the following main features: mathematical texts are formalized using a specific formal language that is close to a natural language of mathematical publications; a proof search is based on special sequent-type calculi formalizing natural reasoning style, such as application of definitions and auxiliary propositions. These calculi also admit a separation of equality handling from deduction that gives an opportunity to integrate logical reasoning with symbolic calculation.

Quantified Interference: Information Theory and Information Flow

The paper investigates which of Shannon’s measures (entropy, conditional entropy, mutual information) is the right one for the task of quantifying information flow in a programming language. We examine earlier relevant contributions from Denning, McLean and Gray and we propose and motivate a specific quantitative definition of information flow. We prove results relating equivalence relations, interference of program variables, independence of random variables and the flow of confidential information. Finally, we show how, in our setting, Shannon’s Perfect Secrecy theorem provides a sufficient condition to determine whether a program leaks confidential information.