[Paper Review] SAT-based Explicit LTL Reasoning

Jianwen Li, Shufang Zhu+2 more|arXiv (Cornell University)|Jul 9, 2015

Formal Methods in Verification19 references4 citations

TL;DR

This paper introduces a SAT-based explicit reasoning framework for Linear Temporal Logic (LTL), replacing traditional tableau-based state and transition construction with SAT solving. The approach, implemented in Aalta_v2.0, outperforms existing LTL satisfiability solvers—including Aalta_v1.2 and NuXmv—by significantly reducing runtime and solving more instances, demonstrating that SAT solving can be more efficient than tableau in explicit LTL reasoning when combined with targeted heuristics.

ABSTRACT

We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly outperforms all existing LTL satisfiability solvers. Furthermore, we show that the framework can be extended from propositional LTL to assertional LTL (where we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and demonstrating that this can yield an exponential improvement in performance.

Motivation & Objective

• To address the computational inefficiency of traditional tableau-based explicit LTL reasoning, which lags behind advances in SAT solving.
• To explore whether SAT solving can be fully leveraged in explicit temporal reasoning, particularly in LTL satisfiability checking.
• To design a new framework that constructs LTL transition systems via SAT solving rather than syntactic tableau decomposition.
• To implement and evaluate a SAT-based LTL satisfiability solver that outperforms existing tools in both speed and scalability.
• To identify and apply heuristics that reduce the state space explosion inherent in pure SAT-based state generation.

Proposed method

• Construct LTL transition systems by encoding temporal constraints as Boolean constraints and solving them via SAT solvers, replacing tableau-based state expansion.
• Use a SAT solver (Minisat) to generate states and transitions explicitly, ensuring correctness through Boolean constraint satisfaction.
• Introduce heuristics such as unsat-core extraction, ELIMINATION, and SAT_PURSUING to reduce the search space and improve performance.
• Implement a lightweight state generation process that avoids the expensive normal-form transformation used in prior tools like Aalta_v1.2.
• Design a $getState$ function that integrates conflict analysis and core extraction to guide state exploration efficiently.
• Extend the framework to assertional LTL, showing exponential performance gains in preliminary evaluations.

Experimental results

Research questions

• RQ1 Can SAT solving be effectively used as the primary engine for explicit LTL reasoning, replacing tableau-based construction?
• RQ2 How does SAT-based state generation compare to tableau-based state generation in terms of state space size and performance?
• RQ3 What heuristics can be applied to SAT-based LTL reasoning to reduce state explosion and improve scalability?
• RQ4 Can a SAT-based explicit LTL satisfiability solver outperform both tableau-based and symbolic SAT-based solvers?
• RQ5 To what extent can the SAT-based framework be extended to other LTL reasoning tasks such as LTL-to-Büchi translation or model checking?

Key findings

• Aalta_v2.0 with heuristics solved 6,750 LTL satisfiability instances, outperforming NuXmv-BMCIMC (6,714), NuXmv-IC3-Klive (6,700), and Aalta_v1.2 (6,689).
• Aalta_v2.0 reduced total runtime by over 23,000 seconds compared to Aalta_v1.2, primarily by avoiding expensive normal-form generation.
• The unsat-core extraction heuristic enabled Aalta_v2.0 to solve all 617 unsatisfiable instances in the benchmark set, including those that previously timed out.
• For satisfiable formulas, the ELIMINATION and SAT_PURSUING heuristics were essential to solve challenging benchmarks like /anzu/amba and /anzu/genbuf.
• Aalta_v2.0 with heuristics solved 617 unsatisfiable instances, outperforming Aalta_v1.2 (309) and ls4 (335), though NuXmv-IC3-Klive solved more (620) in some cases.
• The framework demonstrated exponential performance improvement in assertional LTL, suggesting broader applicability beyond propositional LTL.