Share overlapping leaves in nested SSTL observer synthesis

Develop a more careful construction that shares overlapping leaves when unrolling nested Synchronous Signal Temporal Logic formulas, thereby reducing the exponential growth in observer size with nesting depth.

Background

The observer-synthesis technique unrolls nested bounded SSTL operators into a finite collection of non-nested obligations, represented by leaf observers. Under the naive construction, the number of leaves grows exponentially with nesting depth because each outer operator generates copies of the inner obligations for every tick in its interval. The paper notes that many of these leaves overlap and could potentially share state or computation. Developing such sharing would reduce the size and resource cost of observers for formulas with deep nesting or wide temporal windows, while preserving the same monitoring semantics.

References

The naive unrolling is exponential in nesting depth, but most leaves overlap and could be shared by a more careful construction, which we leave to future work as the present technique already suffices for our case studies.

— Synchronous Observers Revisited for Runtime Verification of Lustre Using STL  (2608.12693 - Kenwright et al., 13 Aug 2026) in Section 4, “N-deep Observer Synthesis,” subsection “Unrolling a nested formula”