Complexity Theory – Do grammars consist only of rules with an icon on each page NL-complete?

The unrestricted grammars characterize the recursively enumerable languages. This is the same as for any unrestricted grammar G There are some Turing machines that can recognize L(G) and vice versa.

Context: grammars are complete. Therefore, complexity classes like NL have equivalents in grammars.

An important NL complete problem is ST connectivity (or "reachability") (Papadimitriou 1994 Thrm. 16.2), the problem of determining whether there is a path from in a directed graph G and two nodes s and t in this graph s to t. ST connectivity can be seen in NL because we start at node s and do not go deterministically to any other node that can be reached. ST connectivity can be considered NL-hard if you look at the computational state graph of another NL algorithm and take into account that the other algorithm accepts if and only if there is a (undetermined) path from the start state to an accepting state.

With a directed graph, decide whether a->b is a directional path is NL-complete.

We will reduce the directed graph to a grammar rule with a symbol on each side:

Add a grammar rule for each directed edge in the diagram. The directed edge a->b becomes the grammar rule a|b.

The NL full query is: "When I hire a Can I derive a symbol for the start symbol? b with the grammar rules? "

Each grammar rule has an icon on each page (i.e. a|b).

Therefore, grammar rules with an icon on each page are NL-complete.

Do grammars consist only of rules with an icon on each page NL-complete?

co.combinatorics – Maximum families with equally long intervals consist of equilateral triangles

My question is a continuation of How do I find n points in a plane so that as many pairs of points as possible have the same distance? – – see the presumption at the end of this post.



To let $ n $ be a positive integer. To let $ e (A) $ be the maximum cardinality
from set $ P subseteq binom A2 $ so that distance $ d (x y) $ is constant
about everything $ {x y } in P. $

To let $ D_n in binom { Bbb R ^ 2} n $ be that
$$ forall_ {A in binom { Bbb R ^ 2} n} quad e (D_n) ge e (A) $$

to adjust $ Delta subseteq binom {D_n} 2 $ so that distance $ d (x y) $ is constant
about everything $ {x y } in Delta $ and $ | Delta | = e (D_n) $ is called critical.

GUESS: To let $ n> 2. $ To let $ Delta in binom {D_n} 2 $ be critical.
Then for everyone $ {x y } in Delta $ there are $ z in D_n $ so that
$ {x z } , text {and} , {y z } , in , Delta. $



I am sure that the following weaker version is actually true. Namely only
Cardinalities $ e (D_n) $ are clearly defined, but not quantities $ D_n. $ Therefore I am confident that the presumption applies to at least one $ D_n $ (for each $ n $)
but – who knows – the guess fails for some $ D_n. $

Should variations of a color within a color palette consist only of shades and shades of that color?

I am designing an IDE with a dark user interface. We have an existing color palette, but our (~ 10) shades of gray appear to be off when applied to the IDE in large quantities that require a dark user interface.

When analyzing the individual color fields, I realized that they do not belong to an HTML color family. Should Variations of a color, within a Good Color palette, do not consist of shades and shades of the same color or family of colors?

To increase my confusion, both material design (https://material.io/resources/color/#!/?view.left=0&view.right=0&primary.color=263238) and human interface guidelines (https: // Developers .apple.com / design / User interface guidelines / ios / visual-design / color /) contain gray palettes with shades of gray from different HTML color families.

Terminology – Is there a name for a diagram whose corner points consist of edges of an existing diagram that are connected by an edge if they have a common corner point?

I was wondering if there is a name for this construction:
Take a graphic $ G $ and construct a new diagram $ G & # 39; $ in which the edges of $ G $ Now vertices and "vertices become edges" in the sense that vertices are connected by edges $ G & # 39; $ when in as edges $ G $ shared a common apex.

A little more precise:
Given a diagram $ G = (V = {v_1, v_2, points, v_n }, E = {e_1, e_2, points, e_k }) $ where everyone $ e_i = {u, v } subset V $ We define the graph $ G & # 39; = (V & # 39; = {e_1, e_2, dots, e_k }, E & # 39;) $ in order to $ {e_i, e_j } in E & # 39; iff e_i cap e_j neq emptyset $,

I don't know if this can be used for anything (I suspect it can't) but it just occurred to me and I thought it might have a name.

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How can you solve 5 equations that only consist of 3 undermined variables?

Suppose that there is a system of five trigonometric equations, among which are three indefinite parameters (eg, x, y, z). In principle, only the solutions of the three parameters that satisfy all five equations are permissible. I have tried to solve only three equations with "NSolve" and also with "FindRoot", of course the later command gives approximate solutions, NSolve took about 18 hours (the equations are too complicated in the expression) to solve the equation system, but the solutions do not satisfy the two remaining equations, indicating inconsistency. Can you please show me a way to solve the three equations, on the condition that the remaining two are fulfilled at the same time? That is, the code generates only the solutions that take all five equations into account. Any help in this regard will be of great help.

Thank you in advance.

Graph Theory – Is there a Ford Fulkerson run for each flownet in which all extension paths consist of forward edges only?

Is there a Ford Fulkerson algorithm for each flownet in which all extension paths consist of forward edges only?

I've seen this claim for a flow network where all edges have c (e) = 1, and I tried to find a counter example for networks with different capacities, but could not.

Is this statement always correct? and if so, do we need reverse edges just because we can not know which paths have only forward edges while we are executing the FF algorithm?

Many Thanks!

Best way to transfer content without 301 to other domain?

Hello,

I have a website that I think might be punished, perhaps because of backlinks or other off-page issues, and I definitely can not say it. But the content is high quality, so I've considered moving it to another domain, but the 301 redirect is likely to enforce all penalties in the current domain. What's the best way to move the current content so that Google does not consider it as a duplicate?

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8 – How can I integrate field groups to consist of multiple paragraph fields in a node?

I have a scenario that resembles the FAQs and would consist of 4 fields:

Section title
…. bodywork ….
public files
private files

These are used to create an agenda. I want the titles of the sections to match the content below them.

I was able to create a field with text, public files, and private files and have it redo in a content type.

What I really want is that this has an extension / contract for the remainder as a field group with the section title. I can not seem to allow multiple field groups in the node.

Example:

  1. Part 1

  2. Section 2

…. is extended to display body, files

  1. Section 3

My goal is to stay within D8 and not need any custom modules. Any thoughts or support? Many thanks.