Real-Time Logics: Complexity and Expressiveness

@article{Alur1993RealTimeLC,
  title={Real-Time Logics: Complexity and Expressiveness},
  author={Rajeev Alur and Thomas A. Henzinger},
  journal={Inf. Comput.},
  year={1993},
  volume={104},
  pages={35-77}
}
The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about real-time systems, we combine this classical theory of infinite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by… 
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References

SHOWING 1-10 OF 88 REFERENCES
Real-time logics: complexity and expressiveness
  • R. Alur, T. Henzinger
  • Philosophy
    [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science
  • 1990
TLDR
A unifying framework for the study of real-time logics is developed, and the underlying classical theory of timed state sequences is identified, it is shown to be nonelementarily decidable, and its complexity and expressiveness are used as a point of reference.
Back to the future: towards a theory of timed regular languages
  • R. Alur, T. Henzinger
  • Computer Science
    Proceedings., 33rd Annual Symposium on Foundations of Computer Science
  • 1992
TLDR
The authors show that the resulting class of bounded two-way deterministic timed automata is closed under all boolean operations, has decidable (PSPACE-complete) emptiness and inclusion problems, and subsumes all decidable real-time logics the authors know.
Logics and Models of Real Time: A Survey
We survey logic-based and automata-based languages and techniques for the specification and verification of real-time systems. In particular, we discuss three syntactic extensions of temporal logic:
Quantitative Temporal Reasoning
TLDR
This work proposes a system of temporal logic, RTCTL (Real-Time Computation Tree Logic), that allows the melding of qualitative temporal assertions together with real-time constraints to permit specification and reasoning at the twin levels of abstraction: qualitative and quantitative.
Suitability of the Propositional Temporal Logic to Express Properties of Real-Time Systems
TLDR
This paper presents abbreviations which allow the expression of the most important real-time properties and some other important requirements of PTL and shows that they are easy to use and that the induced complexity cost is the same as the complexity of the other real- time logics.
The temporal specification and verification of real-time systems
TLDR
The abstract computational model of timed transition systems is introduced as a conservative extension of traditional transition systems: qualitative fairness requirements are superseded by quantitative real-time constraints on the transitions.
The Benefits of Relaxing Punctuality
TLDR
This work introduces a temporal language that can constrain the time difference between events only with finite, yet arbitrary, precision and show the resulting logic to be EXPSPACE-complete.
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency
TLDR
This work proposes a temporal logic for causality and choice in distributed systems based on bisimulation semantics for concurrency and describes a logic for distributed transition systems.
Propositional Dynamic Logic of Nonregular Programs
The complexity of propositional linear temporal logics
We consider the complexity of satisfiability and determination of truth in a particular finite structure for different propositional linear temporal logics. We show that both the above problems are
...
1
2
3
4
5
...