Tudor Jebelean

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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)
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)
We present an algorithm for finding valid polynomial relations (i. e. invariants) among program variables for imperative loops. The algorithm is implemented in the verification environment for imperative programs (using Hoare logic) in the frame of the Theorema system (www.theorema.org). We use techniques from (polynomial) algebra and combinatorics, namely(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)
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)
The speed of integer and rational arithmetic increases significantly by systolic implementation on a SIMD architecture. For multiplication of integers one obtains linear speed-up (up to 29 times), using a serial{parallel scheme. A two-dimensional algorithm for multiplication of polynomials gives half-linear speed-up (up to 383 times). We also implement(More)