Definability with bounded number of bound variables
Information and Computation
Journal of the ACM (JACM)
Real-time logics: complexity and expressiveness
Information and Computation - Special issue: selections from 1990 IEEE symposium on logic in computer science
The benefits of relaxing punctuality
Journal of the ACM (JACM)
On the Ehrenfeucht-Fraïssé Game in Theoretical Computer Science
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
First-order logic with two variables and unary temporal logic
Information and Computation - Special issue: LICS'97
An Until Hierarchy for Temporal Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Back to the future: towards a theory of timed regular languages
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
On Expressiveness and Complexity in Real-Time Model Checking
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Some Recent Results in Metric Temporal Logic
FORMATS '08 Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Unambiguity in timed regular languages: automata and logics
FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
On the expressiveness of TPTL and MTL
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
The unary fragments of metric interval temporal logic: bounded versus lower bound constraints
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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Timed temporal logics exhibit a bewildering diversity of operators and the resulting decidability and expressiveness properties also vary considerably. We study the expressive power of timed logics TPTL[U,S] and MTL[UI, SI] as well as of their several fragments. Extending the LTL EF games of Etessami and Wilke, we define MTL Ehrenfeucht-Fraïssé games on a pair of timed words. Using the associated EF theorem, we show that, expressively, the timed logics BoundedMTL[UI, SI], MTL[FI, PI] and MITL[UI, SI] (respectively incorporating the restrictions of boundedness, unary modalities and non-punctuality), are all pairwise incomparable. As our first main result, we show that MTL[UI, SI] is strictly contained within the freeze logic TPTL[U,S] for both weakly and strictly monotonic timed words, thereby extending the result of Bouyer et al and completing the proof of the original conjecture of Alur and Henziger from 1990. We also relate the expressiveness of a recently proposed deterministic freeze logic TTL[Xθ, Yθ] (with NP-complete satisfiability) to MTL. As our second main result, we show by an explicit reduction that TTL[Xθ, Yθ] lies strictly within the unary, non-punctual logic MITL[FI, PI]. This shows that deterministic freezing with punctuality is expressible in the non-punctual MITL[FI, PI].