Exponential succinctness of multi-clock freeze logics

Establish whether multi-clock freeze logics—specifically the freeze-quantified logic studied in CONCUR 2023 and CONCUR 2025—admit exponentially more succinct representations, by proving or refuting the conjectured exponential succinctness of these logics relative to existing real-time specification formalisms or their automata-based encodings.

Background

The paper introduces MightyPPL, a tool translating Metric Interval Temporal Logic with Past and Pnueli modalities into timed automata, enabling complete verification over timed words. Beyond this, the authors outline future directions that include extending their framework to freeze-quantified fragments of real-time logic, a class where variables can be frozen to timestamps for later comparison.

Within this context, they point to multi-clock freeze logics—citing a specific logic studied in prior work at CONCUR 2023 and CONCUR 2025—as a promising target. The authors explicitly conjecture that these logics may offer exponentially more succinct representations, suggesting that specifications in such logics could be dramatically shorter than in other formalisms (e.g., standard MITL with past and Pnueli modalities) for the same behaviors, which would have significant implications for verification efficiency.