Relate Reynolds’s LTL tableau cycle detection to LNS cycle recognition

Determine the precise relationship between the cycle detection underlying Reynolds’s one-pass tree-shaped tableau for LTL satisfiability, including its LOOP and PRUNE rules, and the cycle-recognition method developed for non-wellfounded linear nested sequent proofs.

Background

The paper compares its cycle-recognition problem with the cycle detection used in Reynolds’s tableau for LTL satisfiability. Both approaches identify recurring structures in proof-search or tableau branches, but they operate in different formalisms: Reynolds’s method uses LOOP and PRUNE rules, whereas the paper recognizes cycles in non-wellfounded linear nested sequent proofs through saturation recurrence, focused traces, and matching end components.

The authors explicitly state that the precise relationship between these approaches has not been established, leaving open whether and how the two cycle-detection mechanisms correspond.