# 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…

## 574 Citations

Logics for Real Time: Decidability and Complexity

- Computer ScienceFundam. Informaticae
- 2004

This work defines a quantitative temporal logic that is based on a simple modality within the framework of monadic predicate Logic that is as expressive as any logic suggested in the literature.

Time-Bounded Verification

- Computer Science, MathematicsCONCUR
- 2009

It is shown that, over bounded time intervals, MTL satisfiability and model checking are EXPSPACE-Complete, whereas these problems are decidable but non-elementary for the predicate logics.

Comparing Expressive Power of Timed Logics BTP report

- Computer Science
- 2012

This work attacks the open problems of comparing MTL with timed past and untimed past, and establishes a hierarchy for MTL, based on the largest constant that can appear in the interval constraints, using EF games.

A Decidable Timeout based Extension of Propositional Linear Temporal Logic

- Computer ScienceArXiv
- 2010

It is proved that when TLTL is interpreted over discrete time, it can be embedded in the monadic second order logic with time, and whenTL is interpreting over dense time without the condition of non-zenoness, the resulting logic becomes $\Sigma_1^1$-complete.

A survey on temporal logics for specifying and verifying real-time systems

- Philosophy, Computer ScienceFrontiers of Computer Science
- 2013

Decidability, axiomatizability, expressiveness, model checking results for each logic analysed are given and a comparison of features of the temporal logics discussed is provided.

Real-time and Probabilistic Temporal Logics: An Overview

- Computer Science, PhilosophyArXiv
- 2010

This paper analyzes real-time and probabilistic temporal logics which have been widely used in this field and extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed.

A Logical Characterization of Timed (non-)Regular Languages

- Computer Science, MathematicsMFCS
- 2014

A monadic theory of orders, extending the one introduced by Kamp, is defined, which is expressively equivalent to CLTLoc, and a decidable extension with an arithmetical next operator, which allows the expression of timed non-ω-regular languages.

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