TLDR: A new technique called “diminution” is introduced to tackle the “grounding bottleneck” in Answer Set Programming (ASP). By selecting a smaller subset of constants from the Herbrand universe, diminution significantly reduces the size of ground programs and improves solving efficiency, making ASP more practical for complex problems. This method integrates seamlessly with existing ASP solvers and has shown substantial performance gains in various benchmarks.
Answer Set Programming (ASP) is a powerful tool used for solving complex problems in various fields, from robotics to logistics. However, despite its expressiveness, ASP often faces a significant challenge known as the “grounding bottleneck.” This occurs because programs with variables need to be fully “instantiated” or “grounded” over their entire set of possible values (called the Herbrand universe) before they can be solved. When the Herbrand universe is very large, this grounding phase can create enormous programs, making them difficult and time-consuming to solve.
To address this critical issue, researchers have introduced a novel concept called “diminution.” Diminution is essentially a carefully selected, smaller subset of the Herbrand universe. Instead of grounding the program over the entire universe, it’s grounded only over this reduced subset. The goal is to generate a much smaller, more manageable ground program without losing the ability to find meaningful solutions.
The paper formally defines diminution and explores its key properties. It introduces concepts like “admissible diminution,” which ensures that any solution found using the reduced program can be extended to a solution of the original, fully grounded program. A stronger notion, “safe diminution,” guarantees that every solution of the original program can be “restricted” to a solution of the diminished program. There’s also “Premain-preserved diminution,” which ensures that essential parts of the solution are always maintained, preventing trivial or incomplete results. For instance, in a graph coloring problem, a diminution might focus on a subset of nodes and colors, but it must still preserve the ability to color the relevant parts of the graph correctly.
Implementing diminution is designed to be seamless with existing ASP solvers. The approach integrates with standard “grounders” (the tools that perform the instantiation) by using “domain predicates.” These are special predicates that restrict variables to only take values from the chosen diminution set. This clever integration means that the technique can be applied without needing to modify the core ASP solvers themselves.
The effectiveness of diminution was rigorously tested across five different benchmarks, including real-world optimization problems like VirtualHome (household robotic planning) and AutomatedWarehouse (multi-robot logistics), as well as classic satisfiability problems like Hamiltonian Circuit and Stable Marriage. For these tests, specific “heuristics” (smart shortcuts) were designed to select the constant subsets. For example, in VirtualHome, a “skeleton plan” generated by AI models helped identify relevant constants. In warehouse scenarios, locations were restricted to areas near objects of interest.
The experimental results were highly promising. When using diminution, the grounding time was significantly reduced, by up to 70% on average. The size of the grounding files, which can often be massive, decreased by an impressive 85%. This translates directly into faster solving times and a much lower rate of “timeouts” (when the solver fails to find a solution within a given time limit). For instance, with the Clingo solver, the VirtualHome timeout rate dropped from 62% to under 5%. Similar improvements were observed with the DLV2 solver. These findings clearly demonstrate that diminution is a robust and general-purpose method for alleviating the grounding bottleneck in ASP, making it more efficient and practical for a wider range of applications.
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In conclusion, diminution offers a powerful and generalizable strategy to tackle the grounding bottleneck in Answer Set Programming. By intelligently reducing the constant set used for grounding, it leads to significantly smaller programs and substantial performance improvements in both grounding and solving times. This innovation paves the way for ASP to be applied more effectively to complex, real-world problems. For more in-depth details, you can refer to the full research paper: Diminution: On Reducing the Size of Grounding ASP Programs.
