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See this answer first: https://cs.stackexchange.com/questions/86422/proving-worst-case-running-time-is-in-omegan2
Understanding the linked answer for insertion sort leads to the following statement. Prove that the statement is either incorrect or correct.
Statement:
If you find $(y)$ for worst case running time ... |
See this answer first: https://cs.stackexchange.com/questions/86422/proving-worst-case-running-time-is-in-omegan2
Understanding the linked answer for insertion sort leads to the following statement. Prove that the statement is either incorrect or correct.
Statement:
If you find $(y)$ for worst case running time ... |
See this answer first: https://cs.stackexchange.com/questions/86422/proving-worst-case-running-time-is-in-omegan2
Understanding the linked answer for insertion sort leads to the following statement. Prove that the statement is either incorrect or correct.
Statement:
If you find $(y)$ for worst case running time ... |
null |
$L_1\in P$ , $L_2\in NP$, is it possible that $L_1\cup L_2 \in P$ |
There is a very simple $O(n \log k)$ algorithm described in *Weighted random sampling with a reservoir* by Pavlos S. Efraimidis and Paul G. Spirakis, which can be summarized as:
> Associate value $r_i^{1/w_i}$ to $a_i$, where $r_i$ is an independent random uniform value on $[0, 1]$. Sort the elements by their associ... |
Let $G_1, \dots, G_m$ be an enumeration of all strongly connected directed graphs on at most $n$ vertices in which every vertex has out-degree 2 (the corresponding edges labelled $a,b$).
The algorithm proceeds in $n^2m$ rounds. In round $(i-1) n^2 + (j-1) n + k$ (where $1 \leq i \leq m$ and $1 \leq j,k \leq n$), the... |
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Is there support in the foundation of mathematics for dimensioned quantities?
Those immersed in real-world software problems, continually confront the absence of dimensioned quantities in programming langauges. This absence appears in the foundation of mathematics!
The absence of support afflicts even Wolfram's ... |
about slicing I would suggest to check following link: [implementation of list slicing][1] and also following answer on [big O of list slicing ][2]. also try to find list_concat method here [source code of cpython][3]. I assume that list-slicing and list_concat that are internal staff of python would be fast because o... |
null |
So I recently learned about dual-port and multi-port RAM but I tried doing some research on modern RAM architectures and if they use it but I couldn't find anything on it. |
Are modern ram architectures (DDR4 or SDRAM) Multi-port or Dual-port? |
|computer-architecture|cpu|memory-hardware| |
Given $N$ a whole number and a set $S$ of divisors of N, where no repetition is allowed. Decide if there is a combination of divisors with a product equal to $N$.
- Remove non-divisors from $S$.
- Remove duplicates from S by using set() in python.
- Treat $S$ as list of non-duplicates and sort from smallest to ... |
I recently read about the “computer” built out of matchboxes designed by Donald Michie that could teach itself how to play tic tax toe. Here is the Wikipedia article about it:
https://en.m.wikipedia.org/wiki/Matchbox_Educable_Noughts_and_Crosses_Engine
I thought it looked interesting, so I decided to make a digit... |
How many games will a “MENACE” tic tax toe computer take to train |
|machine-learning| |
I recently read about the “computer” built out of matchboxes designed by Donald Michie that could teach itself how to play tic tac toe. Here is the Wikipedia article about it:
https://en.m.wikipedia.org/wiki/Matchbox_Educable_Noughts_and_Crosses_Engine
I thought it looked interesting, so I decided to make a digit... |
null |
In Ben-David & et al.'s *Understanding Machine Learning*, the authors wrote:
> Let $\mathcal{H}_n$ be the class of axis aligned rectangles in $\mathbb{R}^n$ , namely,
> $$
\mathcal{H}_n = \{h(a_1,\dots,a_n, b_1,\dots, b_n) :\forall i,a_i \le b_i\}
$$
> where
> $$
h(a_1,\dots,a_n, b_1,\dots, b_n)(x,y)=
\begin{... |
Why we need at most $2n$ examples to determine an axis aligned rectangle |
|machine-learning|learning-theory| |
null |
null |
In the C language, there's the 2 similar-in-form but distict-in-meaning constructs:
`(type)value` which is a casting, and `(value)`, which is a grouping.
How do a $LR(1)$ parser deal with this? I can think of a compiler that breaks syntax and semantic boundary able to disambiguate it by providing information abou... |
How do C compilers distinguish casting from grouping? |
|formal-grammars|ambiguity| |
The primitive recursive functions can be defined in terms of the following five axioms:
1. _Constant function:_ $C_n^k$ is a $k$-ary function that always returns $n$
2. _Successor function:_ $S$ is a 1-ary function $S(x) \mapsto x+1$
3. _Projection function:_ $P^k_i$ is a $k$-ary function that returns its $i$th ar... |
They can easily be distinguished by a compiler: In the first case, the thing in parentheses is a type, in the second case it isn’t.
Now if you insist on parsing based on a grammar only, that may be a problem. But there is no reason why a compiler writer would limit themselves in this way. So how does a compiler do ... |
null |
I have read and understood various proofs, but have not been able to understand precisely why we require $S=\Omega(\log n)$. |
In the proof that $DSPACE(S)\subseteq DTIME(2^O(S))$, why precisely do we require that $S=\Omega(\log n)$ |
|complexity-theory|time-complexity|space-complexity| |
In the proof that $DSPACE(S)\subseteq DTIME(2^{O(S)})$, why precisely do we require that $S=\Omega(\log n)$ |
I recently read about the “computer” built out of matchboxes designed by Donald Michie that could teach itself how to play tic tac toe. Here is the Wikipedia article about it:
https://en.m.wikipedia.org/wiki/Matchbox_Educable_Noughts_and_Crosses_Engine
I thought it looked interesting, so I decided to make a digit... |
Let $G=(V,E)$ be an unweighted directed acyclic graph with a set $V$ of vertices and a set $E$ of edges. The all-pairs shortest path problem can be solved efficiently using the Floyd-Warshall algorithm. The new objective is to find a subset of maximum cardinality $S \subseteq V$ such that for every pair of vertices $v$... |
First of all, we believe that $DSPACE(X) \subseteq DTIME(X)$ is false. As a consequence, $X$ must be chosen so that $X \neq 2^{O(X)}$. Choosing $X = \Omega(\lg n)$ guarantees this. Moreover, it is also consistent with the definition of the complexity classes $L$ and $P$. The former is the class of the languages (or pro... |
First of all, we believe that $DSPACE(X) \subseteq DTIME(X)$ is false. As a consequence, $X$ must be chosen so that $X \neq 2^{O(X)}$. Additionally, we want $ X < 2^{O(X)}$ to allow the Turing machine requiring $X$ space to halt on all of its inputs. Choosing $X = \Omega(\lg n)$ guarantees this. Moreover, it is also c... |
We believe that $DSPACE(X) \subseteq DTIME(X)$ is false. As a consequence, $X$ must be chosen so that $X \neq 2^{O(X)}$. Additionally, we want $ X < 2^{O(X)}$ to allow the Turing machine requiring $X$ space to halt on all of its inputs. Choosing $X = \Omega(\lg n)$ guarantees this. Moreover, it is also consistent with... |
null |
From the internet:
A finite-state machine is formally defined as a 5-tuple (Q, I, Z, ∂, W) such that:
Q = finite set of states
I = finite set of input symbols
Z = finite set of output symbols
∂ = mapping of I x Q into Q called the state transition function, i.e. I x Q → Q
W = mapp... |
Are there infinite state machines, and how do their computational power relate to turing machines? |
|computability|automata| |
null |
null |
Turing machines aren't defined this way is simply because auomata with an infinite number of states aren't [effective](https://en.wikipedia.org/wiki/Effective_method).
The definition of effective procedures tries to capture our intuitive understanding of algorithms, and Turing machines are meant to formalize effective... |
null |
Dimensions play an important role in all natural sciences (physics, chemistry, engineering, etc.), but not in mathematics. The reason is that the property of "having a dimension" is not really a property of a quantity. It is a property of a _physical law_ that involves that quantity. The property is formulated as a con... |
We believe that $DSPACE(X) \subseteq DTIME(X)$ is false. As a consequence, $X$ must be chosen so that $X \neq 2^{O(X)}$. Additionally, considering $DSPACE(X) \subseteq DTIME(Y)$ we want $ Y = 2^{O(X)}$ to allow the Turing machine requiring $X$ space to halt on all of its inputs (if $Y < 2^{O(X)}$ then the Turing machin... |
We believe that $DSPACE(X) \subseteq DTIME(X)$ is false. As a consequence, $X$ must be chosen so that $X \neq 2^{O(X)}$. Additionally, considering $DSPACE(X) \subseteq DTIME(Y)$ we want $ Y = 2^{O(X)}$ to allow the Turing machine requiring $X$ space to halt on all of its inputs: this is because the number of configurat... |
We believe that $DSPACE(X) \subseteq DTIME(X)$ is false. As a consequence, $X$ must be chosen so that $X \neq 2^{O(X)}$. Additionally, considering $DSPACE(X) \subseteq DTIME(Y)$ we want $ Y = 2^{O(X)}$ to allow the Turing machine requiring $X$ space to halt on all of its inputs: this is because the number of configurat... |
null |
I am writing a program in TI Code Composer Studio assembly-only empty project using the MSP-EXP430FR6989. The assembly-only empty project uses MSP430 Assembler Code Template for use with TI Code Composer Studio. Here is the project requirements:
Use the MSP430 seven-segment daughter board to display and multiply two... |
Daughter-board multiplier |
|computer-architecture| |
Is there support in the foundation of mathematics for dimensioned quantities?
Those immersed in real-world software problems, continually confront the absence of dimensioned quantities in programming languages. Occasionally this results in [a billion dollar disaster, such as the Mars Climate Orbiter][1]. This abse... |
null |
Of course there is mathematical support for dimensioned quantities. It's kind of trivial from mathematical point of view.
Off the top of my head, here's a suggestion. Given some basic units of measurement, represented by a set of symbols $U$, say $\lbrace \mathtt{g}, \mathtt{m}, \mathtt{s}\rbrace$ consider the free... |
Consider the scenario where we are given a collection of n integers. These integers are unordered and may include duplicates. Additionally, we have a set of m ranges, each defined by two integers representing the lower and upper boundaries of the interval. Similar to the integers, these intervals are unordered and dupl... |
Optimizing Pairings Between Integers and Intervals for Maximal Matching |
|algorithms| |
Are there any well established algorithms for finding an object's location in 3D space when we know its approximate distance to at least 3 known locations?
Trilateration seems to be a well understood and popular topic and yet the only algorithms I've found come from fringe academic papers. I'm looking for a widely a... |
Well established Trilateration algorithms |
|algorithms| |
null |
It seems that your primary issue is that the way the operators are rendered in the setting of higher order type theory and higher order logic seems a bit forced and conflationary. I tend to agree.
An extension of Curry-Howard that stays entirely within first order logic will use [natural bijections](https://math.sta... |
Turing machines aren't defined this way is simply because automata with an infinite number of states aren't [effective](https://en.wikipedia.org/wiki/Effective_method).
The definition of effective procedures tries to capture our intuitive understanding of algorithms, and Turing machines are meant to formalize effectiv... |
Turing machines aren't defined this way simply because automata with an infinite number of states aren't [effective](https://en.wikipedia.org/wiki/Effective_method).
The definition of effective procedures tries to capture our intuitive understanding of algorithms, and Turing machines are meant to formalize effective c... |
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null |
null |
|algorithms|matching|bipartite-matching|intervals| |
This is a case of bipartite matching between the two parties: the set of integers (let's call it $Z$) and the set of intervals (let's call it $I$). From [Kőnig's theorem](https://en.wikipedia.org/wiki/K%C5%91nig%27s_theorem_(graph_theory)), we know that the maximum possible matching size can be at most $\min(|Z|, |I|)$... |
Consider the case of maximal bipartite matching between the two parties: the set of integers (let's call it $Z$) and the set of intervals (let's call it $I$). From [Kőnig's theorem](https://en.wikipedia.org/wiki/K%C5%91nig%27s_theorem_(graph_theory)), we know that the maximum possible matching size can be at most $\min... |
I have this E-R diagram
[![][1]][1]
[1]: https://i.stack.imgur.com/tNHJi.png
Now im asked to add a entity named as "kiosk".At a kiosk up to 2 items of expedition of different category can be expedited.How do I add this in the E-R diagram?
The category is a attribute of a item of expedition (top left... |
E-R diagram exercise referencing to attribute of another entity |
|relational-algebra| |
It's not possible for an LR(1) parser to solve this problem without using the [Lexer Hack](https://en.wikipedia.org/wiki/Lexer_hack): information from the symbol table, which is able to differentiate type names from variable names, is reported to the parser using two different token kinds for "identifier". The impossi... |
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null |
Firstly, just convert the $\delta_x$ and $\delta_y$ operator into Toeplitz matrix $D_x$ and $D_x$, then the objective is a linear system.
$$
||S-I||_2 + \beta||D_x S - H||_2 + \beta||D_y S - V||_2
$$
You can see the solution
$$
S-I+\beta D_x^T (D_x S-H) + \beta D_y^T (D_y S-V)
$$
yields
$$
(1 + \beta D_x^T D_... |
Firstly, just convert the $\delta_x$ and $\delta_y$ operator into Toeplitz matrix $D_x$ and $D_x$, then the objective is a linear system.
$$
||S-I||_2 + \beta||D_x S - H||_2 + \beta||D_y S - V||_2
$$
You can see the solution
$$
S-I+\beta D_x^T (D_x S-H) + \beta D_y^T (D_y S-V) = 0
$$
yields
$$
(1 + \beta D_x^... |
null |
In "Computational Complexity: A Modern Approach", it states that to prove that $NSPACE(s(n))\subseteq DTIME(2^{O(s(n)})$, we can do the following:
> By enumerating over all possible configurations, we can construct the graph $G_{M,x}$ in $2^{O(s(n)}$ time and check whether $C_{start}$ is connected to $C_{accept}$ in... |
Why exactly does constructing a configuration graph of an $s(n)$ soace bounded NDTM require that $s$ is space-constructible? |
|complexity-theory|time-complexity|space-complexity| |
I need to understand the motivations behind distributed computing, namely the fact to perform a computation by making physically separated computer, connected by communication links, work together.
I am in particular interested in a review explaining their interest in the context of being more resilient to errors (I... |
A pedagogic review on the advantage/drewbacks of distributed computing |
|reference-request|distributed-systems| |
Why exactly does constructing a configuration graph of an $s(n)$ space bounded NDTM require that $s$ is space-constructible? |
Let M be a non-deterministic Turing machine (NDTM) that accepts a language L if and only if:
> * for each $ x\in L $ M doesn't accept x for at most m branch(path) calculations.
> * for each $ x\notin L $ M doesn't reject x for at most m branch calculations.
let M be a Turing machine non deterministic, with one o... |
How to Prove or Disprove Language Acceptance with Limited Error by a Non-Deterministic Turing Machine? |
|formal-languages|turing-machines| |
DDR4 is single-port. DDR5 is also single-port, _but_ it's dual-channel. It can handle two commands at the same time, like dual-port memory. But those commands are expected to arrive over the same physical channel.
This is part electrical engineering (signal integrity at high speeds), part CPU architecture (multi-cor... |
You do indeed have a premise problem. We are not FSMs *or* TMs. Don't forget that all of these computational theory devices are simple mathematical abstractions composed of a series of axioms and limited input. The computational theory systems (Godel's, Turing's, and Church's) are merely designed to allow us to mak... |
I'll build on Pål's answer to be a bit more explicit about how we can code PR functions using those operations. First of all, note that we can code any finite sequence of (positive) numbers into a single number such that the $i$'th element of the sequence can be extracted; for instance, this should be doable by mapping... |
Laslie Lamport is very influential in the field of distributed computation, here is his quote: "A distributed system is one in which the failure of a computer you didn't even know existed can render your own computer unusable'' is a famous Lamport quip. I would suggest check article about [him][1]. he's trying to for... |
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