11,227 research outputs found
Timed Context-Free Temporal Logics
The paper is focused on temporal logics for the description of the behaviour
of real-time pushdown reactive systems. The paper is motivated to bridge
tractable logics specialized for expressing separately dense-time real-time
properties and context-free properties by ensuring decidability and
tractability in the combined setting. To this end we introduce two real-time
linear temporal logics for specifying quantitative timing context-free
requirements in a pointwise semantics setting: Event-Clock Nested Temporal
Logic (EC_NTL) and Nested Metric Temporal Logic (NMTL). The logic EC_NTL is an
extension of both the logic CaRet (a context-free extension of standard LTL)
and Event-Clock Temporal Logic (a tractable real-time logical framework related
to the class of Event-Clock automata). We prove that satisfiability of EC_NTL
and visibly model-checking of Visibly Pushdown Timed Automata (VPTA) against
EC_NTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a
context-free extension of standard Metric Temporal Logic (MTL). It is well
known that satisfiability of future MTL is undecidable when interpreted over
infinite timed words but decidable over finite timed words. On the other hand,
we show that by augmenting future MTL with future context-free temporal
operators, the satisfiability problem turns out to be undecidable also for
finite timed words. On the positive side, we devise a meaningful and decidable
fragment of the logic NMTL which is expressively equivalent to EC_NTL and for
which satisfiability and visibly model-checking of VPTA are EXPTIME-complete.Comment: In Proceedings GandALF 2018, arXiv:1809.02416. arXiv admin note: A
technical report with full details is available at arXiv:1808.0427
On the decidability and complexity of Metric Temporal Logic over finite words
Metric Temporal Logic (MTL) is a prominent specification formalism for
real-time systems. In this paper, we show that the satisfiability problem for
MTL over finite timed words is decidable, with non-primitive recursive
complexity. We also consider the model-checking problem for MTL: whether all
words accepted by a given Alur-Dill timed automaton satisfy a given MTL
formula. We show that this problem is decidable over finite words. Over
infinite words, we show that model checking the safety fragment of MTL--which
includes invariance and time-bounded response properties--is also decidable.
These results are quite surprising in that they contradict various claims to
the contrary that have appeared in the literature
A Metric Encoding for Bounded Model Checking (extended version)
In Bounded Model Checking both the system model and the checked property are
translated into a Boolean formula to be analyzed by a SAT-solver. We introduce
a new encoding technique which is particularly optimized for managing
quantitative future and past metric temporal operators, typically found in
properties of hard real time systems. The encoding is simple and intuitive in
principle, but it is made more complex by the presence, typical of the Bounded
Model Checking technique, of backward and forward loops used to represent an
ultimately periodic infinite domain by a finite structure. We report and
comment on the new encoding technique and on an extensive set of experiments
carried out to assess its feasibility and effectiveness
- …