Technology Category
Constraint Satisfaction and Optimization: SatisfiabilitySearch and Optimization: Mixed Discrete/Continuous SearchKnowledge Representation and Reasoning: Computational Complexity of Reasoning
Planted-solution SAT and Ising benchmarks from integer factorization
🤖 AI Summary
This work proposes a novel family of verifiable benchmarks based on the integer factorization problem to evaluate SAT solvers and Ising optimization algorithms. By encoding the arithmetic constraint of multiplying two primes into conjunctive normal form (CNF) formulas and mapping them to Ising models, the generated instances exhibit clear structure, single-parameter scalability, and built-in ground-truth solutions (p, q), facilitating straightforward verification. The approach integrates logical circuit modeling, efficient CNF encoding, carry compression, and Ising mapping techniques, addressing gaps in existing benchmarks regarding structural clarity and verifiability. Experimental results demonstrate that the median runtime of SAT solvers on these instances grows exponentially with the bit-length of the factors. An open-source instance generator accompanying this work has been publicly released.
Technology Category
Application Category
📝 Abstract
We present a family of planted-solution benchmark instances for satisfiability (SAT) solvers and Ising optimization derived from integer factorization. Given two primes $p$ and $q$, the construction encodes the arithmetic constraints of $N = p \times q$ as a conjunctive normal form (CNF) formula whose satisfying assignments correspond to valid factorizations of~$N$. The known pair $(p,q)$ serves as a built-in ground truth, enabling unambiguous verification of solver output. We show that for two $d$-bit primes the total number of carry contractions is on the order of $d^4$. Empirical benchmarks with SAT solvers show that median runtime grows exponentially in the bit-length of the factors over the range tested. The construction provides a scalable, structured, and verifiable benchmark family controlled by a single parameter, accompanied by open-source generation software.
Problem
Research questions and friction points this paper is trying to address.
planted-solution
SAT benchmarks
Ising optimization
integer factorization
CNF encoding
Innovation
Methods, ideas, or system contributions that make the work stand out.
planted-solution
integer factorization
SAT benchmarks
Ising optimization
CNF encoding
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