Implicit Computation of Filtered Prime Implicants

2026-08-06

AI Summary

This work addresses the scalability limitations of traditional prime implicant computation under constrained input spaces, where explicit post-processing filtering is typically required and often infeasible due to the exponential growth in the number of prime implicants. To overcome this bottleneck, the paper introduces an end-to-end symbolic algorithm that, for the first time, directly embeds contextual or structural constraints into the prime implicant generation process, thereby eliminating the need to explicitly enumerate all prime implicants. Built upon the Coudert-Madre decision diagram framework, the approach achieves implicit filtering through symbolic representation and integrated constraint handling. A modular toolchain is further developed to decouple decision diagram construction, prime implicant computation, and constraint processing. Experimental results demonstrate that the proposed method significantly enhances scalability and effectively mitigates the exponential explosion inherent in large-scale instances.

Abstract

Prime implicants (PIs) are central in computer science, with applications in logic minimization, diagnosis, explainable formal methods and AI. Algorithms for the computation of PIs were first-and-foremost considered on the full input space, not considering the case where the input space might be constrained by context or structural dependencies. To filter out those PIs that do not fulfill the constraints, existing methods rely on an explicit post-processing step after computing all PIs, which leads to scalability issues due to the number of PIs being exponential. We propose end-to-end symbolic algorithms that implicitly represent the set of PIs under side constraints. For this, we extend the prominent Coudert-Madre method based on decision diagrams and implement a modular tool chain that separates decision-diagram construction, PI computation, and filtering.

Problem

• Prime Implicants
• Constraints
• Scalability
• Logic Minimization
• Symbolic Computation

Innovation

• implicit computation
• prime implicants
• decision diagrams
• side constraints
• symbolic algorithms