Testing Positiveness of Polynomials
Journal of Automated Reasoning
On the Shortest Linear Straight-Line Program for Computing Linear Forms
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Finding Efficient Circuits Using SAT-Solvers
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Cardinality Networks and Their Applications
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
A new combinational logic minimization technique with applications to cryptology
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Inferring network invariants automatically
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Grid-based SAT solving with iterative partitioning and clause learning
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Finding efficient circuits for ensemble computation
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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Non-trivial linear straight-line programs over the Galois field of two elements occur frequently in applications such as encryption or high-performance computing. Finding the shortest linear straight-line program for a given set of linear forms is known to be MaxSNP-complete, i.e., there is no ε-approximation for the problem unless P=NP. This paper presents a non-approximative approach for finding the shortest linear straight-line program. In other words, we show how to search for a circuit of XOR gates with the minimal number of such gates. The approach is based on a reduction of the associated decision problem (“Is there a program of length k?”) to satisfiability of propositional logic. Using modern SAT solvers, optimal solutions to interesting problem instances can be obtained.