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Languages with Static Upper Bounds for Resource Consummations

For Topics related to Blockchains and Smart Contracts, I’m developing a programming language that has the property that it is possible to calculate an upper bound on the consumed resources of a function/program during compilation given the resources consumed by its primitive operations are known.

I know that this is possible if you have no Loops (or loops with a statically known number of max iterations) and no recursion and no dynamic dispatched functions. I was wondering if these restrictions can be relaxed further without losing the ability to give an upper bound on resource consumptions.

With an internet search I came up empty and only found information concerning the complexity of a function/program but never methods for computing a concise upper bound.

My questions are:

  • Is there a term for this class of languages that I can use to find existing research?
  • Do you know of existing literature I can consult?

What’s an upper bound for this recurrence so I can take advantage of the Master Theorem?


$ $ T(N) = \begin{cases}1 & \text{if } N = 1\ T(\varphi(N)) + 2T(\sqrt{N}) + \lg(\varphi(N))^3 & \text{otherwise} \end{cases}$ $

where $ \varphi(N)$ is Euler’s totient function. My objective is to find an upper bound so that I can apply the Master Theorem and find a closed-form formula.

How to allow my Visio drawing inside a web part to occupy the whole upper area, as currently I will get an empty upper area

I have a Visio drawing with .vdw , then I used the Visio Web Access web part to add the drawing to my wiki page. I set the following settings for the web part:-

enter image description here

But I will get a free upper area as shown in he below picture:-

enter image description here

Now I can move the mouse on the drawing and drag it to start from the upper area,, but of course I need this change to be permanent,, so can anyone advice on this please


How to prove an implication about an upper bound mentioned in the proof of master theorem?

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How can we prove rigorously the proposition “Suppose the if in case 1 is true, the equation 4.23 is true”? For given constant b and j, the implication in green makes sense. If the upper bound of j was fixed, the equation 4.23 follows directly. However, when n increases, the upper bound of j also increases, though is slower. It is where I find difficult to prove there always exists a value m > 0 such that for all n >= m, equation 4.23 is true.

WordPress 4.4.2 upload give error, can’t write is upper directory allowed to be written

I searched around for this problem en found a lot of ideas most has to do with write access. The idea is: Put all directories in the wp-content/upload to 744 if not work to 755 and all the files to 644 (like this one for example: And some even said 777 looks to me a bit of a over kill but, I tried and it didn’t work as well. I keep getting the some error.

Empty cash of browser and from WordPress it self. Didn’t do the trick.

The rights to the directories is to the user and the root so I would say the the system has all access to the directory. I have ssh access to change if needed.

Even if i write a small code to copy a image from a uploaded image. It made a new directory in wp-content/upload and it did copy the file. But when i try it with WordPress it still fails.

Does anyone has a idea of what I can try more?