Finding Polynomial Invariants for Imperative Loops in the Theorema System (2006)
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@TECHREPORT{Kovács06findingpolynomial,
author = {Laura Ildikó Kovács and Tudor Jebelean},
title = {Finding Polynomial Invariants for Imperative Loops in the Theorema System},
institution = {},
year = {2006}
}
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Abstract
Abstract. 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 Gröbner Bases, variable elimination, algebraic dependencies and symbolic summation (the Gosper algorithm, handling geometric series, C-finite solving). These methods are demonstrated on several examples which have been treated completely automatically by our implementation.
