SMT with Uninterpreted Functions and Monotonicity Constraints in Systems Biology

2026-04-08

AI Summary

This work addresses the problem of inferring models in systems biology that must satisfy monotonicity constraints—requiring certain inputs to exert a consistent positive or negative influence on outputs—by introducing, for the first time, a combination of uninterpreted functions from SMT solving with explicit monotonicity constraints. The authors propose an efficient lazy lemma generation mechanism, integrated with quantifier-aware encoding and an active quantifier instantiation strategy. Evaluated on multiple systems biology benchmarks, the approach significantly outperforms domain-specific tools such as Bonesis (based on Answer Set Programming) and AEON (based on Binary Decision Diagrams), demonstrating superior scalability and solving efficiency, particularly on high-arity and structurally complex instances.

Abstract

The theory of uninterpreted functions is a key modeling tool for systems with unknown or abstracted components. Some domains such as systems biology impose further restrictions regarding monotonicity on these components, requiring specific inputs to have a consistently positive or negative effect on the output. In this paper, we tackle the model inference problem for biological systems by applying the theory of uninterpreted functions with monotonicity constraints. We compare the performance of naive quantified encodings of the problem and the performance of the existing approach based on eager quantifier instantiation, which is based on the fact that a finite set of quantifier-free monotonicity lemmas is sufficient to encode the monotonicity of uninterpreted functions. Additionally, we consider a lazy variant of the approach that introduces the monotonicity lemmas on demand. We evaluate the SMT-based approach to model inference using a large collection of systems biology benchmarks. The results demonstrate that the instantiation-based encodings significantly outperform quantified encodings, which typically struggle with large function arities and complex instances. As the key result, we show that our approach based on SMT with uninterpreted functions and monotonicity constraints significantly outperforms state-of-the-art domain-specific tools used in systems biology, such as the ASP-based Bonesis and the BDD-based AEON.

Problem

• SMT
• uninterpreted functions
• monotonicity constraints
• model inference
• systems biology

Innovation

• SMT
• uninterpreted functions
• monotonicity constraints
• model inference
• systems biology