## Does the Construct Spirit from Summon Construct cast at 4th level have 40 or 55 hp?

I believe that there is a typo in the Summon Construct spell from Tasha’s Cauldron of Everything. The spell is shown as a 4th level spell in the spell listing and in the table at the beginning of the chapter. However, the hit points formula in the Construct Spirit stat block is given as "40 + 15 for each spell level above 3rd," emphasis mine. This is odd because all of the other stat block formulas are formatted such that you only add extra hp if the spell is cast at a higher level.

RAW the construct has 55 HP when cast as a 4th level spell, but have the designers commented that this was unintentional and the base HP should actually be 40?

## Does the metal construct summoned from Summon Construct also cause fire damage when using Slam?

The Summoned Construct’s Heated Body ability is the same wording as the Remorhaz’ (though it does less damage).

Construct Spirit:

Heated Body (Metal Only). A creature that touches the construct or hits it with a melee attack while within 5 feet of it takes 1d10 fire damage.

Remorhaz:

Heated Body. A creature that touches the remorhaz or hits it with a melee attack while within 5 feet of it takes 10 (3d6) fire damage.

but unlike the Remorhaz’ Bite, the construct’s description does not have a clause that it also deals additional (fire) damage on a hit with its Slam.

Construct

Slam. Melee Weapon Attack: your spell attack modifier to hit, reach 5 ft., one target. Hit: 1d8 + 4 + the spell’s level bludgeoning damage.

Remorhaz

Bite. Melee Weapon Attack: +11 to hit, reach 10 ft., one target. Hit: 40 (6d10 + 7) piercing damage plus 10 (3d6) fire damage. If the target is a creature, it is grappled (escape DC 17). Until this grapple ends, the target is restrained, and the remorhaz can’t bite another target.

Does a creature count as touching the construct (and get fire damage) if they are hit by its slam attack?

Info on the Summoned Construct is from Tasha’s Cauldron of everything. Info on Rhemoraz is from Monster Manual

## How can we construct a TM with a Halt1 Oracle that decides if a TM halts on all inputs?

Can we construct an explicit Turing Machine with a Halt1 oracle that decides if a standard Turing Machine halts on all inputs?

By a Halt1 oracle I mean that we have the ability to decide if Turing Machines with a Halting oracle halts or not.

## How can I efficiently construct a CFG from a language

I am new to CFG’s and automata in general and I came across an exercise where I needed to construct a CFG for the language {a^m b^n | n <= m + 3}.

So m can be infinitely bigger than n but n can only be up to 3 more bigger than m and they can be the same. I have no idea how to make a CFG for this.

What I came up with was:

S -> AB | _  A -> a | aa | aaa | C | _  C -> aC | a | _ B -> bB | b | _ 

But I think this is not even close…

Any help/tips/advice would be much appreciated!

## Abalative Armor and Stone Construct Interplay

Abalative Armor provides damage reduction 15/- at 10th level, once the infused item has prevented damage from a single attack even if not all the damage reduction is needed, the magic fades.

Stone Construct provides damage reduction 10/adamantine. Once the spell has prevented a total of 10 points of damage per artificer level you possess (maximum 150 points) it is discharged.

If a creature has damage reduction from more than one source, the two forms of damage reduction do not stack. Instead, the creature gets the benefit of the best damage reduction in a given situation.

My question is does the damage reduced by the Abalative Armor also reduce the total provided by Stone Construct?

Apologies if this question has been asked in the past by another.

## Is it possible to construct a finite state automata for a decimal adder?

Suppose the strings are of the form x#y#z , where x,y,z are strings formed from the alphabet $$\Sigma=(0,1,2,3,4,5,6,7,8,9)$$ . The language is accepted if x+y=z is satisfied, for example : 56#65#121 is accepted, but 2#97#104 is not. Is it possible to find a finite automata for such a language ? I am aware of binary addition but I cannot fathom how decimal addition could be carried out using a DFA .

## Construct a array using following rules

Consider there is a array $$a$$ of length $$n$$ , $$a=[a_i ,0 \leq i \leq n]$$ and all $$a_i>0$$ and I need to construct a array $$b$$ of length $$n$$ (if possible) , $$b=[b_i , 0\leq i \leq n]$$ .Rules for making array b is all $$1\leq b_i\leq 5$$ .

Consider $$j=i+1$$ ,if $$a_j>a_i$$ then $$b_j>b_i$$ ,if $$a_j then $$b_j and if $$a_i=a_j$$ then $$b_i \neq b_j$$ .

Example : $$a=[2,3,4]$$ then $$b$$ can be $$[1,2,3]$$ ,any $$b$$ is $$accepted$$.

My approach is to use a simple $$dynamic$$ $$programming$$ ,$$dp[i][j]$$ where i will check if first $$i$$ elements of $$b$$ can be formed if $$b_i=j$$ where $$0 if it is possible $$dp[i][j]=1$$ else ,$$dp[i][j]=0$$ .By this method i could find if answer exits but i could not find the array $$b$$ ,I know array $$b$$ can be formed by depth first search as we can see states are connected by i have no idea after that.Could anyone help me how to use dfs on this question.

## How to construct an DFA which accept string with at most 2 zeros [duplicate]

I am designing an dfa which accept a string only it has at most 2 zeros. I am stuck in the final state.

## Parallel Matrix Manipulation: find eigenvalues and construct list

I’m having some trouble with the Parallel commands in Mathematica 12.1:

I need to construct a table where its entries are {M, Eigenvalues of X[M]}, where X is a square matrix of dimension N with N big (>3000) and M a parameter. Specifically, I do the following:

AbsoluteTiming[BSg1P = Table[M = m;      {M, #} & /@ (Eigenvalues[N[X]]), {m, -2, 2, 1}];] 

and I compare with

AbsoluteTiming[BSg1P = ParallelTable[M = m;      {M, #} & /@ (Eigenvalues[N[X]]), {m, -2, 2, 1}];] 

The computing time is similar for both cases: the difference is around 6 sec. for a total time of 300 sec., which makes no sense if the parallel evaluation is performed. Since I have 2 processors, I would expect half of the time or a considerable fraction for the computing duration.

Am I doing something wrong? Or is there something about parallelization that I don’t understand?

On the other hand, if I don’t want to use ParallelTable, is there a way to compute the eigenvalues of X[M] in a faster parallel form?

Thanks.

## How can follow this this guide to construct a graph with matrix/reachability

Let’s we have k matrices. For example we have 3 now, where first one is 8×5 ($$a_1$$ x $$b_1$$), second one is 5 x 6 ($$a_2$$ x $$b_2$$) and last one is 6 x 8 ($$a_3$$ x $$b_3$$). And our goal is to figure out if possible to multiply within any given matrices and reach a matrix of dimension x and y, when x and y is given ahead of time. In this example, (8×5) x (5×6) x (6×8), end up a 8×8 matrix. The hints is given, but I cannot visualize. Any more help is appreciated. can understand the first step, but have not idea about the second one.

First, we can define nodes in the graph as the values of each $$a_i$$ and each $$b_i$$, and put an edge from $$a_i$$ to $$b_i$$.

Second, Whenever there is a chain of matrices $$M_{i1},…M_{ik}$$, we can multiply, then x=$$a_{i1}$$ has an edge to $$b_{i1} =a_{i2}$$, and $$a_{i2}$$ has an edge to $$b_{i2}$$ =$$a_{i3}$$, and so on, up until $$b_{ik}$$ =y. So there could be a path from x to y in this graph.

Third, Inversely, for any path from x to y, the edges form a chain of matrices that we can multiply, which create a x x y matrix. therefore, x is reachable from y in the graph iff there is a chain of matrices which from the x x y matrix.

The first step create something like this ?

>  x-->  > n8-->n5 > n5-->n6  > n6-->n8 >   -->y 

What is $$M_{i1}$$, $$a_{i1}$$ and $$b_{i1}$$? How does that differ to $$a_{1}$$ ?