Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
On the Complexity of Constant Propagation
ESOP '01 Proceedings of the 10th European Symposium on Programming Languages and Systems
Polynomial Constants Are Decidable
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Computing polynomial program invariants
Information Processing Letters
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Automatic generation of polynomial invariants of bounded degree using abstract interpretation
Science of Computer Programming
Polynomial approximations of the relational semantics of imperative programs
Science of Computer Programming
Analysis of modular arithmetic
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Interprocedurally analyzing polynomial identities
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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In this paper, we present methods for checking and inferring allvalid polynomial relations in ${\mathbb Z_{2^w}}$. In contrast to the infinite field 茂戮驴, ${\mathbb Z_{2^w}}$ 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.