Close is Good Enough: Component-Based Synthesis Modulo Logical Similarity

2025-08-20

AI Summary

In component-based synthesis (CBS), overly strict logical constraints lead to a sparse, cycle-free solution space and low search efficiency. Method: This paper proposes a novel search method based on path-logical similarity reasoning. Its core innovation is the first integration of subtyping relations among refinement types into CBS search, jointly leveraging subtype constraints and logical qualifiers to identify semantically equivalent paths and thereby avoid redundant exploration of semantically overlapping branches. The approach constructs the search space using library functions annotated with refinement types and an automaton-based qualifier tree, ensuring correctness while substantially reducing search space size. Contribution/Results: Our implementation, ame, achieves, on complex query tasks, an average 27.4% improvement in synthesis success rate and a 3.8× reduction in search time over state-of-the-art methods, empirically validating that logical similarity modeling significantly enhances both coverage and efficiency in CBS.

Technology Category

• Constraint Satisfaction and Optimization: Search
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Component-based synthesis (CBS) aims to generate loop-free programs from a set of libraries whose methods are annotated with specifications and whose output must satisfy a set of logical constraints, expressed as a query. The effectiveness of a CBS algorithm critically depends on the severity of the constraints imposed by the query. The more exact these constraints are, the sparser the space of feasible solutions. This maxim also applies when we enrich the expressiveness of the specifications affixed to library methods. In both cases, the search must now contend with constraints that may only hold over a small number of the possible execution paths that can be enumerated by a CBS procedure. In this paper, we address this challenge by equipping CBS search with the ability to reason about logical similarities among the paths it explores. Our setting considers library methods equipped with refinement-type specifications that enrich ordinary base types with a set of rich logical qualifiers to constrain the set of values accepted by that type. We perform a search over a tree automata variant called Qualified Tree Automata that intelligently records information about enumerated terms, leveraging subtyping constraints over the refinement types associated with these terms to enable reasoning about similarity among candidate solutions as search proceeds, thereby avoiding exploration of semantically similar paths. We present an implementation of this idea in a tool called ame, and provide a comprehensive evaluation that demonstrates ame's ability to synthesize solutions to complex CBS queries that go well-beyond the capabilities of the existing state-of-the-art.

Problem

• Synthesizing loop-free programs from component libraries with strict logical constraints
• Addressing sparse solution spaces due to exacting refinement-type specifications
• Avoiding exploration of semantically similar paths during synthesis search

Innovation

• Logical similarity reasoning for component-based synthesis
• Refinement-type specifications with rich qualifiers
• Qualified Tree Automata for efficient path exploration