Abstract
We present an algorithm for generating all polynomial invariants of P-solvable loops with assignments and nested conditionals. We prove termination of our algorithm. The proof relies on showing that the dimensions of the prime ideals from the minimal decomposition of the ideals generated at an iteration of our algorithm either remain the same or decrease at the next iteration of the algorithm. Our experimental results report that our method takes less iterations and/or time than other polynomial invariant generation techniques.
The author was supported by the Swiss NSF. This research was partly done in the frame of the Transnational Access Programme at RISC, Johannes Kepler University Linz, supported by the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (contract No 026133).
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Kovács, L. (2010). A Complete Invariant Generation Approach for P-solvable Loops . In: Pnueli, A., Virbitskaite, I., Voronkov, A. (eds) Perspectives of Systems Informatics. PSI 2009. Lecture Notes in Computer Science, vol 5947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11486-1_21
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DOI: https://doi.org/10.1007/978-3-642-11486-1_21
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