Solver-Aided Expansion of Loops to Avoid Generate-and-Test

2025-08-11

AI Summary

Constraint modeling languages (e.g., MiniZinc, Essence) traditionally perform loop unrolling of quantified expressions and comprehensions at compile time by exhaustively enumerating all combinations of induction variables, then relying on partial evaluation to prune invalid terms (e.g., true conjuncts or zero-valued summands), resulting in substantial redundant computation. This paper proposes a solver-aided loop unrolling method: during compilation, a constraint solver is invoked to precisely infer the set of valid loop body instances that must be instantiated—thereby avoiding full enumeration and post-hoc filtering. The approach integrates constraint solving, partial evaluation, and semantic analysis of quantified expressions, guaranteeing generation of a logically equivalent constraint model while dramatically improving compilation efficiency for high-selectivity cases. Experiments demonstrate significant speedups in compilation time on large-scale problems, achieving, for the first time, semantics-driven selective unrolling at compile time.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Constraint modelling languages like MiniZinc and Essence rely on unrolling loops (in the form of quantified expressions and comprehensions) during compilation. Standard approaches generate all combinations of induction variables and use partial evaluation to discard those that simplify to identity elements of associative-commutative operators (e.g. true for conjunction, 0 for summation). This can be inefficient for problems where most combinations are ultimately irrelevant. We present a method that avoids full enumeration by using a solver to compute only the combinations required to generate the final set of constraints. The resulting model is identical to that produced by conventional flattening, but compilation can be significantly faster. This improves the efficiency of translating high-level user models into solver-ready form, particularly when induction variables range over large domains with selective preconditions.

Problem

• Avoids full enumeration of loop combinations
• Uses solver to compute required constraints
• Improves efficiency in model compilation

Innovation

• Solver-aided loop expansion avoids full enumeration
• Computes only required constraint combinations
• Improves compilation speed for large domains