On the Expressiveness of TPTL and MTL over ω-Data Words

@inproceedings{Carapelle2014OnTE,
  title={On the Expressiveness of TPTL and MTL over $\omega$-Data Words},
  author={Claudia Carapelle and Shiguang Feng and Oliver Fern{\'a}ndez Gil and Karin Quaas},
  year={2014}
}
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent extensions of Linear Temporal Logic to specify properties about data languages. In this paper, we consider the class of data languages of non-monotonic data words over the natural numbers. We prove that, in this setting, TPTL is strictly more expressive than MTL. To this end, we introduce 

Path Checking for MTL and TPTL over Data Words

The results yield the precise complexity of model checking deterministic one-counter machines against formulae of MTL and TPTL and prove that the path-checking problem for MTL is P-complete, whereas the Path checking problem for T PTL is PSPACE-complete.

The expressive power, satisfiability and path checking problems of MTL and TPTL over non-monotonic data words

The expressive power, satisfiability problems and path checking problems for MLT and TPTL over all data words are studied, and Ehrenfeucht-Fraisse games for MTL and T PTL are introduced.

A Weighted MSO Logic with Storage Behaviour and Its Büchi-Elgot-Trakhtenbrot Theorem

A weighted MSO-logic in which one outermost existential quantification over behaviours of a storage type is allowed is introduced and it is proved that this logic is expressively equivalent to weighted automata with storage.

References

SHOWING 1-10 OF 18 REFERENCES

Satisfiability for MTL and TPTL over Non-monotonic Data Words

It is proved that the satisfiability problem for many reasonably expressive fragments of MTL and TPTL is undecidable, and thus the use of these logics is rather limited.

On the Expressiveness of TPTL and MTL

This paper positively answer a 15-year-old conjecture that TPTL is strictly more expressive than MTL, and shows that T PTL formulae using only the F modality can be translated into MTL.

Real-time logics: complexity and expressiveness

  • R. AlurT. Henzinger
  • Philosophy
    [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science
  • 1990
Two elementary real-time temporal logics are identified as expressively complete fragments of the theory of timed state sequences, and these two formalisms are well-suited for the specification and verification of real- time systems.

Two-variable logic on data words

This article shows that satisfiability for the two-variable fragment FO2(∼,<,+1) of first-order logic with data equality test ∼ is decidable over finite and infinite data words.

A really temporal logic

  • R. AlurT. Henzinger
  • Computer Science
    30th Annual Symposium on Foundations of Computer Science
  • 1989
TPTL is demonstrated to be both a natural specification language and a suitable formalism for verification and synthesis and several generalizations of TPTL are shown to be highly undecidable.

Automata and Logics for Words and Trees over an Infinite Alphabet

This paper survey several know results on automata and logics manipulating data words and data trees, the focus being on their relative expressive power and decidability.

Model Checking Languages of Data Words

This work considers the model-checking problem for data multi-pushdown automata (DMPA), and states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.

LTL with the Freeze Quantifier and Register Automata

It is proved that surprisingly, over infinite data words, LTLdarr without the 'until' operator, as well as nonemptiness of one-way universal register automata, are undecidable even when there is only 1 register.

On the freeze quantifier in constraint LTL: decidability and complexity

On Expressive Powers of Timed Logics: Comparing Boundedness, Non-punctuality, and Deterministic Freezing

This paper defines MTL Ehrenfeucht-Fraisse games on a pair of timed words and relates the expressiveness of a recently proposed deterministic freeze logic TTL[Xθ, Yθ] to MTL, and shows that deterministic freezing with punctuality is expressible in the non-punctual MITL[FI, PI].