Boolean goal variables

Gold definitionUpdated Apr 2, 2026

Definition

Boolean goal variables are introduced in symbolic algorithms for LTLf synthesis to compactly represent exponentially many combinations of potentially conflicting properties. They enable efficient computation of realizable goal sets and synthesis of strategies achieving maximal sets.

At a glance

Executive summary

Boolean goal variables are a clever way to handle many complex goals in AI planning and control, especially when not all goals can be met at once. They allow algorithms to quickly figure out which goals are achievable and how to achieve the most possible, making the process much faster than older methods.

TL;DR

Boolean goal variables help AI systems efficiently manage and achieve the most possible goals, even when some goals conflict, by representing many options compactly.

Key points

Compactly represent exponentially many goal combinations using Boolean variables in a symbolic algorithm.
Enables LTLf synthesis with multiple, potentially conflicting properties, finding maximal realizable goal sets without enumeration.
Used by researchers and engineers in formal methods, automated planning, and control synthesis.
Substantially outperforms enumeration-based baselines, achieving up to two orders of magnitude speedup.
Focus on efficient symbolic methods for complex logical synthesis problems, especially with partial satisfiability.

Use cases

Automated Planning: Synthesizing plans for robots with multiple, potentially conflicting mission objectives (e.g., "reach location A" and "avoid obstacle B").
Control System Design: Designing controllers for autonomous vehicles that must balance safety, efficiency, and comfort, where not all ideal conditions can always be met.
Software Verification: Generating system specifications or test cases where the system must satisfy a set of properties, but some might be mutually exclusive under certain conditions.
Cyber-Physical Systems: Synthesizing policies for smart grids or industrial automation where multiple operational goals (e.g., energy efficiency, stability, production throughput) need to be optimized.