4,247 research outputs found
Robust, Expressive, and Quantitative Linear Temporal Logics: Pick any Two for Free
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited expressiveness, the lack of quantitative features, and the inability to express robustness. There is work on overcoming these shortcomings, but each of these is typically addressed in isolation. This is insufficient for applications where all shortcomings manifest themselves simultaneously. Here, we tackle this issue by introducing logics that address more than one shortcoming. To this end, we combine the logics Linear Dynamic Logic, Prompt-LTL, and robust LTL, each addressing one aspect, to new logics. For all combinations of two aspects, the resulting logic has the same desirable algorithmic properties as plain LTL. In particular, the highly efficient algorithmic backends that have been developed for LTL are also applicable to these new logics. Finally, we discuss how to address all three aspects simultaneously
Robust, expressive, and quantitative linear temporal logics: Pick any two for free
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified, including limited expressiveness, the lack of quantitative features, and the inability to express robustness. While there is work on overcoming these shortcomings, each of these is typically addressed in isolation, which is insufficient for any application in which all shortcomings manifest themselves simultaneously.
Here, we tackle this issue by introducing logics that address more than one shortcoming. To this end, we combine Linear Dynamic Logic, Prompt-LTL, and robust LTL, each addressing one aspect, to new logics. The resulting logics have the same desirable algorithmic properties as plain LTL for all combinations of two aspects. In particular, the highly efficient algorithmic backends developed for LTL are also applicable to these new logics. Finally, we discuss how to address all three aspects simultaneously
Lukasiewicz mu-Calculus
We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations
Robust Linear Temporal Logic
Although it is widely accepted that every system should be robust, in the
sense that "small" violations of environment assumptions should lead to "small"
violations of system guarantees, it is less clear how to make this intuitive
notion of robustness mathematically precise. In this paper, we address this
problem by developing a robust version of Linear Temporal Logic (LTL), which we
call robust LTL and denote by rLTL. Formulas in rLTL are syntactically
identical to LTL formulas but are endowed with a many-valued semantics that
encodes robustness. In particular, the semantics of the rLTL formula is such that a "small" violation of the environment
assumption is guaranteed to only produce a "small" violation of the
system guarantee . In addition to introducing rLTL, we study the
verification and synthesis problems for this logic: similarly to LTL, we show
that both problems are decidable, that the verification problem can be solved
in time exponential in the number of subformulas of the rLTL formula at hand,
and that the synthesis problem can be solved in doubly exponential time
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