## Is there an abstract architecture equivalent to Von Neumann’s for Lambda expressions?

In other words, was a physical implementation modelling lambda calculus (so not built on top of a Von Neumann machine) ever devised? Even if just on paper?
If there was, what was it? Did we make use of its concepts somewhere practical (where it can be looked into and studied further)?

— I’m aware of specialised LISP machines. They were equipped with certain hardware components that made them better but eventually they were still the same at their core.

If there isn’t such thing, what stops it from being relevant or worth the effort? Is it just a silly thought to diverge so greatly from the current hardware and still manage to create a general-purpose computer?

## Are these REs equivalent?

I have to implement a compiler for a given language as part of an assignment. The language is kept simple enough such that it can be fully expressed through REs.

My question lies with two of the REs provided:

DIGIT := [0-9]?

INTEGER_LITERAL := DIGIT DIGIT*

When I saw the RE for INTEGER_LITERAL I sort of thought to myself:

“Well that’s just DIGIT+”

Am I right to think so?

## To what extent is an x86 machine equivalent to a Turing Machine?

This following partially answers this question, Since “C” is not Turing complete, then “C” is not totally equivalent to a Turing Machine: Is C actually Turing-complete? only because “C” can not access unlimited memory.

It would seem that “C” would be equivalent to a Turing Machine for the set of decidable computations for both as the Church-Turing indicates: “Every effective computation can be carried out by a Turing machine.”

In other words it would seem that anything decidable for an x86 machine must necessarily be decidable for a Turing Machine. Is this correct?

## How are metric TSP and Eulerian cycle equivalent?

In paper : https://arxiv.org/pdf/1908.00227.pdf it is stated that

In the metric TSP problem, which we study here, the distances satisfy the triangle inequality. Therefore the problem is equivalent to finding a closed Eulerian connected walk of minimum cost.

They don’t seem to be equivalent at all, since for a complete graph of size 5, with all edge costs 1, a metric TSP solution would be of cost (and length) 5, whereas an Eulerian cycle would be of cost (and length) 10. Am I misunderstanding?

## Is there an celestial equivalent to an imp/quasit?

Introduced in the early editions of D&D, imps and quasits were presented as devil/demon familiar options for evil spellcasters, and as of fifth edition, this aspect of them hasn’t changed.

However, I could never find a similar creature that was good aligned, or more appropriately, tied to celestial creatures/plane that can act as a familiar. Is there one?

If one such creature doesn’t exist, it is good enough to present good-aligned extraplanar creatures that share similar traits to imps/quasits such as:

• Is Tiny
• Low level/CR

## Find equivalent LL(1) grammar

There is sample question to calculate equivalent LL(1) grammar for below grammar:

$$S \rightarrow S b$$

$$S \rightarrow S d$$

$$S \rightarrow c S$$

$$S \rightarrow c c a$$

At first step, it has left recursion so I remove it and convert it to bellow grammar:

$$S \rightarrow F M$$

$$F \rightarrow c S$$ (same as $$F \rightarrow c F M$$)

$$F \rightarrow c c a$$

$$M \rightarrow \epsilon$$

$$M \rightarrow b M$$

$$M \rightarrow d M$$

We can remove first collision of second and third part too:

$$S \rightarrow F M$$

$$F \rightarrow c D$$

$$D \rightarrow F M$$ (same as $$D \rightarrow c D M$$)

$$D \rightarrow c a$$

$$M \rightarrow \epsilon$$

$$M \rightarrow b M$$

$$M \rightarrow d M$$

One more time remove first collision:

$$S \rightarrow F M$$ (predict: c)

$$F \rightarrow c D$$ (predict: c)

$$D \rightarrow c G$$ (predict: c)

$$G \rightarrow D M$$ (predict: c)

$$G \rightarrow a$$ (predict: a)

$$M \rightarrow \epsilon$$ (predict: b, d, $) $$M \rightarrow b M$$ (predict: b) $$M \rightarrow d M$$ (predict: d) Everything is solved except last part of grammar. I tried to solve it but I think there is no LL(1) grammar for this. Is it true? If not, Is it possible to help me? Thanks. ## Most secure linux equivalent to Shadow Defender for live CD-like nonpersistency with no traces left (or traces that are encrypted) Virtualisation can do reasonably secure nonpersistent drives. Would rather not rely on this alone but also have a host that is nonpersistent too. A live DVD as a host leaves no traces and is physically impossible to permanently infect/own but not very practical to carry around. A live USB flash drive is more practical. Another option is grub2 configured to boot from an ISO image in an internal hard drive. In Windows there is Shadow Defender that intercepts all writes to disk and makes them nonpersistent by storing deltas instead. The deltas are stored in an encrypted format so in the event of a power-down they cannot be recovered easily. This software is hard to bypass because it uses a driver stub that loads very early in the boot sequence. What can one do in linux that is as securely nonpersistent as Shadow Defender or better? Is grub2 boot from an ISO image as effective? Are bootable USB flash drives made with Rufus given any bootable ISO image as effective? What about fsprotect, is it any better than grub2 boot from an ISO image? Anything else? Distros proposed for the host: anything hardened like Pure OS, Astra Linux, Kodachi. Preferably Secure Boot signed. Which is the most hardened option? ## in the lambda calculus with products and sums is$f : [n] \to [n]\beta\eta$equivalent to$f^{n!}$? $$\eta$$-reduction is often described as arising from the desire for functions which are point-wise equal to be syntactically equal. In a simply typed calculus with products it is sufficient, but when sums are involved I fail to see how to reduce point-wise equal functions to a common term. For example, it is easy to verify that any function $$f: (1+1) \to (1+1)$$ is point-wise equal to $$\lambda x.f(fx)$$, or more generally $$f$$ is point-wise equal to $$f^{n!}$$ when $$f: A \to A$$ and $$A$$ has exactly $$n$$ inhabitants. Is it possible to reduce $$f^{n!}$$ to $$f$$? If not, is there an extension of the simply typed calculus which allows this reduction? ## Redirect all subdomains from one root, to the equivalent subdomain of another root? I have foo.com and bar.com I want sub.foo.com to redirect (not be aliased with) sub.bar.com, same for asdf.foo.com and asdf.bar.com, etc, for all sub domains. I know I can redirect all subdomains of foo.com to a particular subdomain of bar.com (e.g. sub.foo.com & asdf.foo.com both go to www.bar.com) using a wildcard DNS record, but I am not aware of how to maintain the requested subdomain name and apply it with the redirect. Is this even possible? ## Is arithmetic coding restricted to powers of$2\$ in denominator equivalent to Huffman coding?

With restriction to $$\frac{k}{2^n}$$ as line segment ends, does arithmetic coding degrade to Huffman coding? As far as I can tell, each symbol will be encoded with an integer amount of bits, which is the same as Huffman coding. However, I’m not sure how to prove that arithmetic coding with this restriction is optimal for integer code lengths.