70 research outputs found
Bounded Satisfiability for PCTL
While model checking PCTL for Markov chains is decidable in polynomial-time,
the decidability of PCTL satisfiability, as well as its finite model property,
are long standing open problems. While general satisfiability is an intriguing
challenge from a purely theoretical point of view, we argue that general
solutions would not be of interest to practitioners: such solutions could be
too big to be implementable or even infinite. Inspired by bounded synthesis
techniques, we turn to the more applied problem of seeking models of a bounded
size: we restrict our search to implementable -- and therefore reasonably
simple -- models. We propose a procedure to decide whether or not a given PCTL
formula has an implementable model by reducing it to an SMT problem. We have
implemented our techniques and found that they can be applied to the practical
problem of sanity checking -- a procedure that allows a system designer to
check whether their formula has an unexpectedly small model
Robust degradation and enhancement of robot mission behaviour in unpredictable environments
© 2015 ACM.Temporal logic based approaches that automatically generate controllers have been shown to be useful for mission level planning of motion, surveillance and navigation, among others. These approaches critically rely on the validity of the environment models used for synthesis. Yet simplifying assumptions are inevitable to reduce complexity and provide mission-level guarantees; no plan can guarantee results in a model of a world in which everything can go wrong. In this paper, we show how our approach, which reduces reliance on a single model by introducing a stack of models, can endow systems with incremental guarantees based on increasingly strengthened assumptions, supporting graceful degradation when the environment does not behave as expected, and progressive enhancement when it does
Approximating Optimal Bounds in Prompt-LTL Realizability in Doubly-exponential Time
We consider the optimization variant of the realizability problem for Prompt
Linear Temporal Logic, an extension of Linear Temporal Logic (LTL) by the
prompt eventually operator whose scope is bounded by some parameter. In the
realizability optimization problem, one is interested in computing the minimal
such bound that allows to realize a given specification. It is known that this
problem is solvable in triply-exponential time, but not whether it can be done
in doubly-exponential time, i.e., whether it is just as hard as solving LTL
realizability.
We take a step towards resolving this problem by showing that the optimum can
be approximated within a factor of two in doubly-exponential time. Also, we
report on a proof-of-concept implementation of the algorithm based on bounded
LTL synthesis, which computes the smallest implementation of a given
specification. In our experiments, we observe a tradeoff between the size of
the implementation and the bound it realizes. We investigate this tradeoff in
the general case and prove upper bounds, which reduce the search space for the
algorithm, and matching lower bounds.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
- …