Abstract-Statistical Model Checking (SMC) is a computationally very efficient verification technique based on selective system sampling. One well identified shortcoming of SMC is that, unlike probabilistic model checking, it cannot be applied to systems featuring nondeterminism, such as Markov Decision Processes (MDP). We address this limitation by developing an algorithm that resolves nondeterminism probabilistically, and then uses multiple rounds of sampling and Reinforcement Learning to provably improve resolutions of nondeterminism with respect to satisfying a Bounded Linear Temporal Logic (BLTL) property. Our algorithm thus reduces an MDP to a fully probabilistic Markov chain on which SMC may be applied to give an approximate solution to the problem of checking the probabilistic BLTL property. We integrate our algorithm in a parallelised modification of the PRISM simulation framework. Extensive validation with both new and PRISM benchmarks demonstrates that the approach scales very well in scenarios where symbolic algorithms fail to do so.
Environmental concerns related to the use of synthetic iron chelates, usually non-biodegradable, for overcoming iron chlorosis motivates the search for alternative compounds. Thus, the main aim of this work was to evaluate siderophore, azotochelin, and a siderophore mimic, N-dihydroxy-N,N’-diisopropylhexanediamide (DPH) as potential sources of iron to cucumber plants grown in hydroponic cultures. The behavior of the iron chelates of azotochelin and DPH, as a substrate of ferric chelate reductase (FCR) and the ability as iron suppliers for chlorotic plants was studied and compared with o,o-EDDHA/Fe3+ and EDTA/Fe3+ chelates, traditionally used for this purpose. The rate of reduction of DPH/Fe3+, by FCR, was comparable to o,o-EDDHA/Fe3+ but lesser than the obtained for EDTA/Fe+3. The rate of reduction for azotochelin/Fe3+ was not possible to determine. Both azotochelin/Fe3+ and DPH/Fe3+ chelates were effective in supplying iron to cucumber plants. After 7 and 21 days, all the plants treated with the iron chelates (10 µM, Fe) of DPH and azotochelin showed significantly higher SPAD index, leaf dry weight and leaf Fe concentration than the control plants (2µM, Fe). In conclusion, azotochelin/Fe3+ and DPH/Fe3+ can be considered as iron sources for cucumber plants when growing in hydroponic culture.
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