Prime implicant computation using satisfiability algorithms
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- TL;DR
- This paper presents a new model and algorithms for computing minimum-size prime implicants of propositional formulas, which are useful in fields like automated reasoning and electronic design automation.
- Problem
- Not specified in the abstract.
- Method
- The authors propose an integer linear program (ILP) formulation to compute minimum-size prime implicants, alongside two new ILP-solving algorithms built on top of a propositional satisfiability (SAT) solver.
- Results
- Experiments on several benchmark examples show that the proposed approach is significantly more efficient than existing solutions.
- Contributions
- The work introduces a simplified ILP formulation and two new SAT-based ILP algorithms that implement advanced search techniques, including non-chronological backtracking, clause recording, and necessary assignment identification.
- Limitations
- Not specified in the abstract.
- Takeaways
- Leveraging satisfiability algorithms to solve integer linear programming formulations provides a significantly more efficient way to compute minimum-size prime implicants.
- Applications
- Automated reasoning, non-monotonic reasoning, and electronic design automation.
- Topics
- Prime implicants, propositional satisfiability (SAT), integer linear programming (ILP).
- For industry
- Electronic design automation and related high-tech engineering sectors.
- Why it matters
- Improves the efficiency of computing prime implicants, benefiting various scientific and engineering applications that rely on logical reasoning.
Abstract
The computation of prime implicants has several and significant applications in different areas, including automated reasoning, non-monotonic reasoning, electronic design automation, among others. The authors describe a new model and algorithm for computing minimum-size prime implicants of propositional formulas. The proposed approach is based on creating an integer linear program (ILP) formulation for computing the minimum-size prime implicant, which simplifies existing formulations. In addition, they introduce two new algorithms for solving ILPs, both of which are built on top of an algorithm for propositional satisfiability (SAT). Given the organization of the proposed SAT algorithm, the resulting ILP procedures implement powerful search pruning techniques, including a non-chronological backtracking search strategy, clause recording procedures and identification of necessary assignments. Experimental results, obtained on several benchmark examples, indicate that the proposed model and algorithms are significantly more efficient than other existing solutions.