| Summary: | This thesis proposes a new method for solving systems of linear constraints over the rational and real numbers (or, equivalently, linear programming) - the conflict resolution method. The method is a new approach to a classic problem in mathematics and computer science, that has been known since the 19th century. The problem has a wide range of real-life applications of increasing importance in both academic and industrial areas. Although, the problem has been a subject of intensive research for the past two centuries only a handful of methods had been developed for solving it. Consequently, new results in this field may be of particular value, not mentioning the development of new approaches. The motivation of our research did not arise solely from the field of linear programming, but rather was instantiated from problems of Satisfiability Modulo Theories (or shortly SMT). SMT is a new and rapidly developing branch of automated reasoning dedicated to reasoning in first-order logic with (combination) of various theories, such as, linear real and integer arithmetic, theory of arrays, equality and uninterpreted functions, and others. The role of linear arithmetic in solving SMT problems is very significant, since a considerable part of SMT problems arising from real-life applications involve theories of linear real and integer arithmetic. Reasoning on such instances incorporates reasoning in linear arithmetic. Our research spanned the fields of SMT and linear programming. We propose a method, that is not only used for solving linear programming problems, but also is well-suited to SMT framework. Namely, there are certain requirements imposed on theory reasoners when they are integrated in SMT solving. Our conflict resolution method possesses all the attributes necessary for integration into SMT. As the experimental evaluation of the method has shown, the method is very promising and competitive to the existing ones.
|
|---|
