Learn More
Theorema is a project that aims at supporting the entire process of mathematical theory exploration within one coherent logic and software system. This survey paper illustrates the style of Theorema-supported mathematical theory exploration by a case study (the automated synthesis of an algorithm for the construction of Gröbner Bases) and gives an overview(More)
The Theorema project aims at extending current computer algebra systems by facilities for supporting mathematical proving. The present early-prototype version of the The-orema software system is implemented in Mathematica 3.0. The system consists of a general higher-order predicate logic prover and a collection of special provers that call each other(More)
A generalization of the binary algorithm for operation at 'word level " by using a new concept of 'modular conjugates " computes the GCD of multiprecision integers two times faster than Lehmer–Euclid method. Most importantly, however, the new algorithm is suitable for systolic parallelization, in 'least-significant digits jirst " pipelined manner and for(More)
Ich erkläre an Eides statt, daß ich die vorliegende Dissertation selbstständig und ohne fremde Hilfe verfaßt, andere als die angegebenen Quellen und Hilfsmittel nicht benutzt bzw. die wörtlich oder sinngemäß entnommenen Stellen als solche kenntlich gemacht habe. Abstract This thesis presents algebraic and combinatorial approaches for reasoning about(More)
versity of Technology) are in general accessible through the World Wide Web. This workshop delves into all aspects of termination of processes. Though the halting of computer programs is undecidable, methods of establishing termination play a fundamental role in many applications and the challenges are both practical and theoretical. From a practical point(More)
Most of the properties established during program verification are either invariants or depend crucially on invariants. The effectiveness of automated verification of (imperative) programs is therefore sensitive to the ease with which invariants, even trivial ones, can be automatically deduced. We present a method for invariant generation that relies on(More)
— We present an algorithm that generates automatically (algebraic) invariant properties of a loop with conditionals. In the proposed algorithm program analysis is performed in order to transform the code into a form for which algebraic and combinatorial techniques can be applied to obtain invariant properties. These invariants are then used for verifying(More)