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- W131466369 abstract "In this paper, we present methods for checking and inferring allvalid polynomial relations in ${mathbb Z_{2^w}}$. In contrast to the infinite field i¾?, ${mathbb Z_{2^w}}$ is finite and hence allows for finitely many polynomial functions only. In this paper we show, that checking the validity of a polynomial invariant over ${mathbb Z_{2^w}}$ is, though decidable, only PSPACE-complete. Apart from the impracticable algorithm for the theoretical upper bound, we present a feasible algorithm for verifying polynomial invariants over ${mathbb Z_{2^w}}$ which runs in polynomial time if the number of program variables is bounded by a constant. In this case, we also obtain a polynomial-time algorithm for inferring all polynomial relations. In general, our approach provides us with a feasible algorithm to infer all polynomial invariants up to a low degree." @default.
- W131466369 created "2016-06-24" @default.
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- W131466369 date "2008-07-13" @default.
- W131466369 modified "2023-09-26" @default.
- W131466369 title "Analysing All Polynomial Equations in ${mathbb Z_{2^w}}$" @default.
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- W131466369 doi "https://doi.org/10.1007/978-3-540-69166-2_20" @default.
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