id int64 1 141k | title stringlengths 15 150 | body stringlengths 43 35.6k | tags stringlengths 1 118 | label int64 0 1 |
|---|---|---|---|---|
5,033 | Could I simulate the implementation of memory components | <p>I am currently reading the IEEE paper <a href="http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1705612" rel="nofollow noreferrer">A Memory-Efficient Parallel String Matching
Architecture for High-Speed Intrusion Detection</a> by Kai Zheng, Bin Liu, Xin Zhang, and Yunhao Liu. </p>

<p>In the paper... | computer architecture simulation | 0 |
5,036 | Alternative to Hamming distance for permutations | <p>I have two strings, where one is a permutation of the other. I was wondering if there is an alternative to <a href="http://en.wikipedia.org/wiki/Hamming_distance">Hamming distance</a> where instead of finding the minimum number of substitutions required, it would find the minimum number of translocations required to... | terminology string metrics permutations edit distance | 1 |
5,039 | How to identify a binary tree uniquely if its Inorder, Preorder and Postorder traversal is given? | <blockquote>
 <p><strong>Possible Duplicate:</strong><br>
 <a href="https://cs.stackexchange.com/questions/439/which-combinations-of-pre-post-and-in-order-sequentialisation-are-unique">Which combinations of pre-, post- and in-order sequentialisation are unique?</a> </p>
</blockquote>



<... | data structures binary trees | 0 |
5,040 | What is the difference between bounding and pruning in branch-and-bound algorithms? | <p>Could anybody please explain what the difference between "bounding" and "pruning" in branch and bound algorithms is?</p>

<p>I'd also appreciate references (preferably books), where this distinction is made clear.</p>
 | algorithms terminology branch and bound | 1 |
5,042 | Indirection in IAS computer | <p>From <a href="http://rads.stackoverflow.com/amzn/click/013293633X">Computer Organisation and Architecture</a>: </p>

<blockquote>
 <p>The IAS operates by repetitively performing an instruction cycle. Each
 instruction cycle consists of two sub cycles. During a fetch cycle,
 the opcode of the n... | computer architecture | 1 |
5,043 | What is the difference between E-Science Infrastructures and Distributed Computing Infrastructures? | <p>What is the difference between eScience infrastructures and grid computing or distributed computing infrastructures? And what are some of their examples.</p>

<p>I can not distinguish them clearly. Is it how a grid is used make it an e-science platform?</p>
 | distributed systems | 0 |
6,046 | What is a good resource to learn about oriented matroids in the context of digraphs and optimization? | <p>I am interested in <a href="http://en.wikipedia.org/wiki/Oriented_matroid" rel="nofollow">oriented matroids</a> in the context of directed graphs and optimization. Unfortunately, I know very little of the topic. Is there a book, article or a resource that serves as a good introduction to oriented matroids, especiall... | optimization reference request discrete mathematics matroids | 1 |
6,048 | Why floating point representation uses a sign bit instead of 2's complement to indicate negative numbers | <p>Consider a fixed point representation which can be regarded as a degenerate case of a floating number. It is entirely possible to use 2's complement for negative numbers. But why is a sign bit necessary for floating point numbers, shouldn't mantissa bits be using 2's complements?</p>

<p>Also why do the expo... | computer architecture floating point number formats | 0 |
6,053 | Convert table look-up into function | <p>Two problems: Given a known table (boolean or int), convert it to a function that returns the same value using only simple operations (and, or, xor, sum...). For example:</p>

<p><code>bool table1[] = {0,1}</code> converted to <code>fun (int index) {return index;}</code></p>

<p><code>bool table2[] =... | algorithms data structures | 0 |
6,055 | Compute relational composition in $O(|E||V|)$ | <p>Definitions: Let $G=(V,E)$ be a DAG without self-loops, and $X \subseteq G$ and $Y \subseteq G$ be graphs.</p>

<p>Input: $X,Y$. Output: The relational composition <a href="http://en.wikipedia.org/wiki/Relation_composition">relational composition</a> $X \circ Y$ in $\mathcal{O}(|E||V|)$.</p>

<ul>&#x... | algorithms graphs algorithm analysis check my algorithm | 1 |
6,058 | How can lazy learning systems simultaneously solve multiple problems? | <p>On the english Wikipedia <a href="http://en.wikipedia.org/wiki/Lazy_learning" rel="nofollow">it says about lazy learning systems</a>:</p>

<blockquote>
 <p>Because the target function is approximated locally for each query to the system, lazy learning systems can simultaneously solve multiple problems [... | terminology machine learning | 1 |
6,062 | Sensor Cover Problem | <p>We are given an interval $I$ and several points $p_1,p_2,...,p_n$. We are also given a set of sensors. Each sensor can be represented by an interval on the same line, which means all points lie within the interval can be monitored by the corresponding sensor. The sensors may not have the equal range.</p>

<p... | algorithms computational geometry | 0 |
6,063 | How to prove that DFAs from NFAs can have exponential number of states? | <p>All non-deterministic finite automata can be turned into equivalent deterministic finite automata. However, a deterministic finite automata only allows a single arrow per symbol pointing from a state. Therefore, its states should be members of the power set of states of the NFA. This seems to indicate that the numbe... | automata finite automata nondeterminism | 1 |
6,067 | What is the difference between operator and function? | <p>We have operator and operands, function and formal arguments. Is the difference purely lexical (we use alphanumerics for funciton identifiers but identify operators with special characters, e.g. "+" and ">=") or it is syntactical, like <a href="http://newsgroups.derkeiler.com/Archive/Comp/comp.lang.vhdl/2012-10/msg0... | terminology programming languages | 1 |
6,072 | Why is Uniform cost search called "uniform" cost search? | <p>By <a href="https://math.stackexchange.com/questions/112734/in-what-sense-is-uniform-cost-search-uniform">this</a> possibly good attempt to explain this, the "uniformity" in the Uniform cost search <em>is actually the uniformity of the heuristic function</em>.</p>

<p>Is this explanation correct ? If yes, th... | terminology artificial intelligence search algorithms heuristics | 1 |
6,075 | How to prove $(n+1)! = O(2^{(2^n)})$ | <p>I am trying to prove $(n+1)! = O(2^{(2^n)})$. I am trying to use L'Hospital rule but I am stuck with infinite derivatives.</p>

<p>Can anyone tell me how i can prove this?</p>
 | asymptotics mathematical analysis landau notation | 1 |
6,076 | Longest range with sum smaller than K | <blockquote>
 <p><strong>Possible Duplicate:</strong><br>
 <a href="https://cs.stackexchange.com/questions/4994/dynamic-programming-table-for-finding-similar-substrings-is-too-large">Dynamic programming table for finding similar substrings is too large</a> </p>
</blockquote>



<p>Say I h... | subsequences | 0 |
6,078 | A d-ary heap problem from CLRS | <p>I got confused while solving the following problem (questions 1–3).</p>

<h3>Question</h3>

<blockquote>
 <p>A <em>d</em>-ary heap is like a binary heap, but(with one possible exception) non-leaf nodes have <em>d</em> children instead of 2 children.</p>
 
 <ol>
 <li><p>How would y... | data structures time complexity runtime analysis | 1 |
6,085 | Average number of comparisons to locate item in BST | <p>This is a GRE practice question. </p>

<p><img src="https://i.stack.imgur.com/dUavw.png" alt="BST n=8"></p>

<p>If a node in the binary search tree above is to be located by binary tree search, what is the expected number of comparisons required to locate one of the items (nodes) in the tree chosen a... | algorithm analysis data structures binary trees search trees average case | 1 |
6,086 | Which of the following regular expressions generate(s) no string with two consecutive 1’s? | <p>This is a GRE practice question. </p>

<p>Which of the following regular expressions generate(s) no string with two consecutive 1’s? (Note that ε denotes the empty string.)</p>

<p>I. (1 + ε)(01 + 0)* </p>

<p>II. (01+10)*</p>

<p>III. (0+1)*(0+ε)</p>

<p>(A) I only</p>
&#... | regular expressions | 1 |
6,088 | Decidability of a problem concerning polynomials | <p>I have come across the following interesting problem: let $p,q$ be polynomials over the field of real numbers, and let us suppose that their coefficients are all integer (that is, there is a finite exact representation of these polynomials). If needed, we may suppose that the degree of both polynomials is equal. Let... | computability undecidability computer algebra | 1 |
6,093 | Formulating a linear program s.t. only extreme point solutions are found | <p>If there are many solutions to a linear program s.t. the objective function is minimized/maximized (= optimal solutions are on an edge of the polytope), how can I force an LP solver to find only an extreme point solution?</p>
 | optimization linear programming | 0 |
6,100 | Find an undecidable language that is mapping-reducible to its complement | <p>As the title suggests. Also, such a language must satisfy that neither it nor its complement are semi-decidable. I already know that $All_{TM}, EQ_{TM}, T$ (that is the set of all deciders) satisfy this property. But I tried reducing these to their complements directly, and via some sort of intermediate language, bu... | computability reductions | 0 |
6,103 | How to make NFA remember its first step? | <p>I have to design an NFA that will take the strings <code>"token"</code> and <code>token</code>.</p>

<p>I can use $\lambda$ or <code>"</code> to the first state, but then how do I know on the final state if it should have end quotes or not?</p>
 | automata finite automata | 0 |
6,108 | Are all context-sensitive languages decidable? | <p>I was going through the <a href="http://en.wikipedia.org/wiki/Context-sensitive_language">Wikipedia definition of <em>context-sensitive language</em></a> and I found this:</p>

<blockquote>
 <p>Each category of languages is a proper subset of the category directly above it. Any automaton and any grammar... | formal grammars turing machines undecidability context sensitive | 1 |
6,111 | How can I reduce Subset Sum to Partition? | <p>Maybe this is quite simple but I have some trouble to get this reduction. I want to reduce <a href="http://en.wikipedia.org/wiki/Subset_sum_problem">Subset Sum</a> to <a href="http://en.wikipedia.org/wiki/Partition_problem">Partition</a> but at this time I don't see the relation!</p>

<p>Is it possible to r... | complexity theory np complete reductions | 1 |
6,114 | Represent string as concatenations | <p>If $S_1,S_2$ are set of strings, then $S_1S_2 = \{s_1s_2|s_1\in S_1, s_2\in S_2\}$. $S^0=\{\epsilon\}$, $\epsilon$ is the empty string. $S^n = S^{n-1}S$. </p>

<p>Two related problems about represent string as concatenation of other strings. </p>

<ol>
<li><p>Given a finite set $S$ of strings, ho... | algorithms formal languages strings | 1 |
6,115 | What's a fast algorithm to decide whether there is an $A_G$ corresponding to a given $\chi_G(\lambda)$? | <p>Given an adjacency matrix <span class="math-container">$A_G$</span> of an undirected graph <span class="math-container">$G$</span>, it is easy and straightforward to compute the characteristic polynomial <span class="math-container">$\chi_G(\lambda)$</span>. What about the other way around? The problem can be formul... | algorithms graphs discrete mathematics matrices | 1 |
6,116 | Given a truth table, force a contradiction | <p>Suppose I have a formula, and a lying witness is attempting to make it evaluate to False.</p>

<blockquote>
 <p>Given a <a href="http://en.wikipedia.org/wiki/Truth_table" rel="nofollow">truth table</a> $c(F_1,…, F_n)$, how could you force a lying
 witness to contradict herself?</p>
</blockquot... | complexity theory computability np complete closure properties decision problem | 0 |
6,117 | determine if a machine prints a certain string in less time than it takes to run the machine itself? | <p>Does there exist a procedure that determines if a polytime machine prints a certain string, and does so in less time than the machine itself takes to run?</p>

<p>Define a machine $a$ that analyzes another machine $b$, input $i$, and string $r$:</p>

<p>$a(b,i,r) = b(i) \text{ prints } r$  ... | complexity theory time complexity turing machines | 0 |
6,119 | How to convert process / cpu core based upon MIPS? | <p>I want to know how can i find number of cpu cores/processor supported given i have the MIPS value?</p>

<p>For e.g I want to know the number of matching cores/processor to process speed of 18 triilion instructions / sec.</p>
 | computer architecture | 0 |
6,120 | Determine interference factors in parallel computing | <p>Parallel processes interfere with each other in many ways, by competing for shared resources such as shared caches, memory, disks, etc.</p>

<p>Would it be possible to determine latent factors just with a runtime analysis, by means of comparing the runtime of the respective applications while running them ma... | parallel computing cpu cache performance | 0 |
6,122 | How to show that f(x) is primitive recursive? | <blockquote>
 <p>Let </p>
 
 <p>$$f(x)=\begin{cases} x \quad \text{if Goldbach's conjecture is true
 }\\ 0 \quad \text{otherwise}\end{cases}$$</p>
 
 <p>Show that f(x) is primitive recursive.</p>
</blockquote>

<p>I know a primitive recursive function is obtained by composition ... | computability recursion | 1 |
6,125 | When would best first search be worse than breadth first search? | <p>I am studying <a href="http://en.wikipedia.org/wiki/Best-first_search" rel="noreferrer">best first search</a> as it compares to BFS (breadth-first search) and DFS (depth-first search), but I don't know when BFS is better than best-first search. So, my question is </p>

<blockquote>
 <p>When would best-f... | graphs artificial intelligence search algorithms | 1 |
6,126 | Asymptotic time complexity of a two-loop program | <p>I have two pieces of code in a function which I'm trying to calculate the asymptotic running time for:</p>

<pre><code>for (int x = 0; x < y; x++) {
 total += total;
 total += x;
}
</code></pre>

<p>and:</p>

<pre><code>while (y > 0) {
 total -= y;
... | time complexity imperative programming loops | 0 |
6,128 | Complement of HAMPATH | <p>Is the complement of the <a href="http://en.wikipedia.org/wiki/Hamiltonian_path" rel="nofollow">Hamiltonian Path problem</a> known to be in $\mathsf{NP}$? I could not find explanations saying that it is, but then neither were there any claims saying that it is <strong>not</strong> in $\mathsf{NP}$.</p>
 | complexity theory decision problem | 1 |
6,129 | Runtime analysis of a nested loop | <p>I have some difficulties performing the worst case analysis on this algorithm.<br>
The outermost loop is executed $2N$ times.<br>
The while loop, in the worst case, will increase by $2$ each time, so it performs $i/2$ basic operations ($*2$ because double call)</p>

<pre><code>for (i=1; i<=2*N; i+... | algorithms algorithm analysis runtime analysis loops | 0 |
6,132 | Superpolynomial time set such that SP=NSP is known? | <p>Are there any superpolynomial time set $\mathsf{SP}$ in between $\mathsf{P}$ and $\mathsf{EXPTIME}$ such that the problem $\mathsf{SP}=\mathsf{NSP}$ has a known answer?</p>

<p><strong>UPDATE</strong>: It must be defined by time and strictly between $\mathsf{P}$ and $\mathsf{EXPTIME}$. I was wondering, what ... | complexity theory nondeterminism | 0 |
6,134 | Are there are problems in NP that have been shown to be not NP-complete but it is still not known if they are in P or not? | <p>I am not talking about NP-indeterminate class because those problems have to be shown to not exist either in P or NP-complete class and existence of such problems proves P!=NP. I am interested to know if we are half-way there i.e. problems that have been proven to be not NP-complete but are in NP but we don't know i... | complexity theory np p vs np | 0 |
6,138 | Problem with implementing Brzozowski's algorithm | <p>I've been trying to implement Brzozowski's algorithm but I've just discovered that it creates suboptimal automata for a certain class of inputs, having one more state than what is really needed in the result. I can show it on a trivial automaton:</p>

<pre><code> a b a b a b ... | algorithms automata finite automata | 1 |
6,139 | Universality of NOT and CNOT | <p>I'm trying to figure out why NOT and CNOT gates are not sufficient to create all bijective functions in classical circuits. I have been struggling on this for hours, and just can't make sense of it.</p>

<p>I feel it has something to do with the Toffoli gate, as it contains an (implicit) AND operation, and I... | logic circuits | 1 |
6,140 | Providing Tight Example in Approximation Algorithm Analysis | <p>Let's say I found a 2-approximation algorithm for a certain problem and I want to show that the analysis is tight. </p>

<p>Do I now need to come up with an example of generic size $n$ or does it suffice to show that I have an example of size $10$ for which the algorithm yields $2OPT$?</p>
 | algorithms proof techniques approximation | 0 |
6,144 | Rigorous proof against pseudo random function | <p>I have the following problem:</p>

<p>Define the keyed function F as follows: On input k ∈ {0, 1}$^n$
and x ∈ {0, 1}$^n$ , Fk(x) = k ⊕ x.Rigorously prove that F is not a pseudorandom function.</p>

<p>How do I approach a proof against pseudorandomness for a keyed function? I don't know where to st... | proof techniques cryptography | 1 |
6,146 | Lower bounds: queues that return their min elements in $O(1)$ time | <p>First, consider this simple problem --- design a data structure of <em>comparable</em> elements that behaves just like a stack (in particular, push(), pop() and top() take constant time), but can also return its min value in $O(1)$ time, without removing it from the stack. This is easy by maintaining a second stack ... | data structures priority queues lower bounds | 1 |
6,147 | Radon transform for advanced 3d graphics and games? | <p>The <a href="https://en.wikipedia.org/wiki/Radon_transform" rel="nofollow">Radon transform</a> is used to take 2d projections of an object and create a 3d representation.</p>

<p>It seems like it would be possible to apply such a transform in 3d graphics in games (although possibly too slow to be practical).... | algorithms computational geometry efficiency graphics | 0 |
6,150 | Designing context free grammar for a language with range restriction on repetition of alphabets | <p>I am having issue with designing contex free grammar for the following language:</p>

<p>$L = \{0^n 1^m \, | \, 2n \leq m \leq 3n \}$ </p>

<p>I can design for the individual cases i.e. for $m \geq 2n$ and $m \leq 3n$ but don't know how should i combine both. Or is it a different approach altogether?... | context free | 1 |
6,154 | Given the phrase "Where NONE of the following are TRUE" and two statements how should a boolean logic be composed? | <p>Let's have two statements</p>

<ol>
<li><strong>(value > 10)</strong></li>
<li><strong>(value < 25)</strong></li>
</ol>

<p>And a list of items with the following values</p>

<ul>
<li>10</li>
<li>20</li>
<li>30</li>
</ul>

<p>This is what a truth table w... | logic | 1 |
6,155 | Using Queues for a Stack and Stacks for a Queue | <p>I was asked a question on how to use a pair of Queues to create a Stack and how to use a pair of Stacks to create a Queue. Any thoughts on how I would do this? Right now I don't even know where to start.</p>
 | data structures queues stacks | 0 |
6,158 | Dynamic Programming Solution for Optimal Matrix Chain Multiplication Order | <p>I have been thinking about why the dynamic programming approach to finding the optimal matrix chain order is better than a brute force approach that finds the optimal order by exploring all nested orders. The more I think about it, the more I feel strongly that the dynamic programming solution considers all possible... | dynamic programming matrices | 0 |
6,161 | What is the depth of a complete binary tree with $N$ nodes? | <p>This question uses the following definition of a complete binary tree<sup>†</sup>:</p>

<blockquote>
 <p>A binary tree $T$ with $N$ levels is complete if all levels except possibly the last are completely full, and the last level has all its nodes to the left side.</p>
</blockquote>

<p>The ... | data structures binary trees | 1 |
6,163 | A context-free grammar for all strings that end in b and have an even number of bs | <p>I'm trying to find CFG's that generate a regular language over the alphabet {a b}</p>

<p>I believe I got this one right: All strings that end in b and have an <strong>even</strong> number of b's in total:</p>

<p>$\qquad S \to SS \\
\qquad S \to YbYb \mid \varepsilon \\
\qquad Y \to aY \mid ... | regular languages formal grammars context free | 1 |
6,167 | If a Language is Non-Recognizable then what about its complement? | <p>Is the complement of a Non-Recognizable language</p>

<ol>
<li>Recognizable</li>
<li>Non-Recognizable</li>
<li>May be Recognizable, May be Non-recognizable. I.e cant comment.</li>
</ol>

<p>A mathematical proof would be of great help since im unable to think of any way to prove this.<... | computability turing machines | 1 |
6,169 | Extreme instancing for computer graphics | <p>Instancing in GPU's, from my little knowledge, simply draw the same object at multiple locations. Each "instance" is just a copy of the same model at a different location. Any local effects, such as animation, would effect all instances. The performance improvement comes from gpu being able to deal with virtually al... | graphics computer games | 0 |
6,170 | How to do Fairy Chess problem in O(N^3)? | <p><a href="https://www.interviewstreet.com/challenges/dashboard/#problem/4f1c88e0dec8a" rel="nofollow">https://www.interviewstreet.com/challenges/dashboard/#problem/4f1c88e0dec8a</a></p>

<blockquote>
 <p>Fairy Chess (35 Points)</p>
 
 <p>You have a $N \times N$ chess board. An $S$-leaper is a c... | algorithms data structures dynamic programming | 0 |
6,173 | Given many partial orders, check them for consistency and report any that are not consistent | <p><strong>Inputs.</strong> I am given a finite set $S$ of symbols. I know there should exist some total order $<$ on $S$, but I'm not given this ordering and it could be anything.</p>

<p>I am also given a collection of assertions. Each assertion takes the form $s_1<s_2<\cdots<s_m$, where $s_1,\d... | algorithms graphs approximation finite sets partial order | 0 |
6,174 | Spot the formalism (some kind of process logic) | <p>Consider the following specification technique.</p>

<p>A specification consists of a finite set of triples $\langle C, A, C' \rangle$,
where $A$ is the name of an action and $C, C'$ are conditions, that is,
propositional formulas over propositional variables.</p>

<p>Example rules (in a more... | logic model checking linear temporal logic hoare logic | 0 |
6,176 | Finding big O notation of function with two parameters | <p>I'm looking to work out the big-O notation for the following:</p>

<p>$$\frac{n^{s + 1} - 1}{n - 1} - 1$$</p>

<p>I have a feeling the result is $O\left( n^s \right)$ but I'm not sure how to prove it.</p>

<p>Any help greatly appreciated! :)</p>
 | time complexity | 1 |
6,178 | Mersenne twister middle word | <p>In some literature, as well as in <a href="http://en.wikipedia.org/wiki/Mersenne_twister" rel="nofollow">Wikipedia</a>, the middle term parameter <em>m</em> of Mersenne twister is called "number of parallel sequences". Why? What is meant here by "parallel sequences"?</p>
 | terminology cryptography pseudo random generators | 0 |
6,179 | Average number of full nodes in a binary search tree | <blockquote>
<p>Let <span class="math-container">$f(N)$</span> be the average number of full nodes (nodes with two children) in an <span class="math-container">$N$</span>-node binary search tree.</p>
<ol>
<li><p>Determine the values of <span class="math-container">$f(0)$</span> and <span class="math-contain... | data structures combinatorics recurrence relation binary trees | 0 |
6,186 | A variant of the Assignment Problem | <p>In my variant of the assignment problem I have a set $A$ of agents and a set (of possibly different cardinality) $T$ of tasks. Each agent needs to be assigned exactly $n$ or $n+1$ tasks, and each task needs to be assigned to exactly $m$ or $m+1$ agents.</p>

<p>It is guaranteed this this is possible: the seg... | optimization linear programming assignment problem | 0 |
6,187 | Program compilation and execution flow | <p>I was studying operating system concepts from <a href="http://rads.stackoverflow.com/amzn/click/0471417432" rel="nofollow noreferrer">Silberschatz, Galvin and Gagne's book</a> (sixth edition) and I have some questions about the flow of execution of a program. A figure explains the processing of the user program:</p>... | compilers operating systems memory management virtual memory | 1 |
6,192 | Explanation of recursive structure of Van Emde Boas Tree | <p>From <a href="http://fileadmin.cs.lth.se/cs/Personal/Rolf_Karlsson/lect12.pdf" rel="nofollow">Van Emde Boas trees lecture</a>:</p>

<blockquote>
 <p>We will use the idea of superimposing a tree of degree ${u^{1/2}}$ on top of
 a bit vector, but <strong>shrink the universe size recursively</strong> ... | algorithms data structures algorithm analysis search trees trees | 1 |
6,193 | Size of the universe for van Emde Boas Trees | <p>In order to achieve the time complexity of $O(\log \log u)$ for van Emde Boas trees I read in <a href="http://fileadmin.cs.lth.se/cs/Personal/Rolf_Karlsson/lect12.pdf" rel="nofollow">this lecture</a> that the the universe size $u$ is chosen as $u = 2^{2^k}$ for some integer $k$ for van Emde Boas trees. Why choose ... | algorithms data structures algorithm analysis binary trees trees | 1 |
6,200 | Using Amdahl's law how do you determine execution time after an improvement? | <p>Speeding up a new floating-point unit by 2 slows down data cache accesses by a factor of 2/3 (or a 1.5 slowdown for data caches). If old FP unit took 20% of program's execution time and data cache accesses took 10% of program's execution time, what is the overall speed up? </p>

<p>I solved this problem usi... | computer architecture program optimization | 1 |
6,202 | Maximum Schedulable Set Zero-Lateness Deadline Scheduling | <p>This is a homework problem for my introduction to algorithms course.</p>

<blockquote>
 <p>Recall the scheduling problem from Section 4.2 in which we sought to
 minimize the maximum lateness. There are $n$ jobs, each with a deadline
 $d_i$ and a required processing time $t_i$, and all jobs are... | algorithms time complexity dynamic programming efficiency scheduling | 0 |
6,206 | What does 'computable in the limit from above' mean? | <p>$H(x)$ is the program size complexity of $x$ for some universal Turing machine $U$. $H$ is not computable, however $H$ is "<em>computable in the limit from above</em>".</p>

<p>From my notes:</p>

<blockquote>
 <p>i.e the set $\{(x,n) \mid x \in B^*,n \geq 0, H(x) \leq n\}$ is computably enumera... | computability terminology | 1 |
6,207 | How to prove transitivity in small-o of asymptotic analysis? | <p>Here is my proof, but I am not sure whether it is correct.</p>

<p>We know:</p>

<p>$\qquad \begin{array}{l}
 \forall {c_1},\exists {n_1},0 \le f\left( n \right) \le {c_1}g\left( n \right),\forall n \ge {n_1} \\ 
 \forall {c_1},\exists {n_2},0 \le g\left( n \right) \le {c_1}h\left( n \right),... | asymptotics check my proof | 0 |
6,208 | Heuristic for Finding Multiple Goals in Graph - e.g. using Kruskals Algorithm | <p>I'm a none-computer-science-student and get some knowledge on AI by taking the CS188.1x Course (Artificial Intelligence) on www.edx.org .</p>

<p>Currently, I am working on the "Search in Pacman" Project; the sources can be found online at <a href="http://www-inst.eecs.berkeley.edu/~cs188/pacman/projects/sea... | algorithms graphs heuristics search problem | 0 |
6,210 | Assignment problem for multiple days | <p>I have a problem that can be reduced to an assignment problem.
(In a previous <a href="https://cstheory.stackexchange.com/questions/12850/matching-on-bipartite-graph-multiple-edges">question</a> i found out how to do that.)</p>

<p>Which means we have a set $A$ of agents and a set $T$ of tasks as well as... | algorithms graphs assignment problem | 1 |
6,211 | How can I improve my Algorithm? | <blockquote>
 <p>This is a problem from Interview Street in Dynamic Programming section.
 <a href="https://www.interviewstreet.com/challenges/dashboard/#problem/4f2c2e3780aeb" rel="nofollow">https://www.interviewstreet.com/challenges/dashboard/#problem/4f2c2e3780aeb</a></p>
 
 <p>Billboards(20 point... | algorithms data structures dynamic programming | 1 |
6,218 | Proving following problem NP Hard using known NP Hard partition problem | <p>Least cost travel by intermixing different airline routes having linear discount functions:</p>

<p>Lowest air fare route chosen by mixing different routes provided by different airline having different discount functions (like some airline can give 25% discount if fare crosses $5k) so that total cost of tra... | complexity theory graphs | 0 |
6,221 | Classfication of randomized algorithms | <p>From <a href="http://en.wikipedia.org/wiki/Randomized_algorithm">Wikipedia</a> about randomized algorithms</p>

<blockquote>
 <p>One has to distinguish between <strong>algorithms</strong> that use the random
 input to reduce the expected running time or memory usage, but always
 terminate with... | algorithms terminology randomized algorithms nondeterminism machine models | 1 |
6,230 | What is tail recursion? | <p>I know the general concept of recursion. I came across the concept of <strong>tail recursion</strong> while studying the quicksort algorithm. In this <a href="http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-046j-introduction-to-algorithms-sma-5503-fall-2005/video-lectures/lecture-4-quickso... | algorithms reference request recursion | 1 |
6,234 | Min cost max flow in bipartite run time | <p>I have a bipartite graph with $|E|=O(|V|^2)$, a super-source and a super-sink. I am looking for the min-cost max-flow (the max-flow of all possible max-flows that has the minimum cost).</p>

<p>For the sake of my question, denote $n=|E|$.</p>

<p>Are there algorithms that will run in $O(n^2)$, or eve... | graphs optimization | 0 |
6,235 | How can we reduce variables when converting from 3-SAT to 4-SAT? | <p>If we suppose that we'd like to convert an instance of 3-SAT to an instance of 4-SAT, by how much can we reduce the amount of variables?</p>

<p><strong>CONVERSION METHODS FOR PRODUCTS OF SUMS</strong></p>

<p>If we are given a 3-SAT clause $(A \lor B \lor C)$, we can readily convert this to 4-SAT by... | satisfiability 3 sat | 0 |
6,236 | Minimum space needed to sort a stream of integers | <p>This question has gotten a lot of attention on SO:<br>
<a href="https://stackoverflow.com/questions/12748246/sorting-1-million-8-digit-numbers-in-1mb-of-ram">Sorting 1 million 8-digit numbers in 1MB of RAM</a></p>

<p>The problem is to sort a stream of 1 million 8-digit numbers (integers in the range $[0... | algorithms sorting space complexity data compression streaming algorithm | 1 |
6,237 | What units should Shannon entropy be measured in? | <p>The only examples I've seen use bits as a measurement of entropy, but all these examples happen to use binary code alphabets. If we wanted to see how well a coding with a code alphabet of length n works, would we measure entropy in units of n?</p>

<p>Or would it make sense to stay using bits if we're compar... | information theory entropy | 1 |
6,239 | Constructing deterministic PDA for not regular language | <p>Let the input alphabet be $\Sigma = \{a,b,c\}$ and <em>L</em> be the language of all words in which all of the <em>a</em>’s come before all of the <em>b</em>’s and there are the same number of <em>a</em>’s as <em>b</em>'s and arbitrarily many <em>c</em>’s that can be in front, behind or among the <em>a</em>’s and <e... | automata pushdown automata | 1 |
6,241 | In the Miller-Rabin primality test, for a composite number, why are at least $\frac{3}{4}$ of the bases witnesses of compositeness? | <p>The following is an excerpt from the <a href="http://en.wikipedia.org/wiki/Miller-Rabin_primality_test#Accuracy_of_the_test" rel="nofollow">Wikipedia article on the Miller-Rabin primality test</a>:</p>

<blockquote>
 <p>It can be shown that for any odd composite $n$, at least $\frac{3}{4}$ of the bases ... | cryptography number theory | 1 |
6,244 | Rényi entropy at infinity or min-entropy | <p>I'm reading a paper that refers to the limit as n goes to infinity of Rényi entropy. It defines it as ${{H}_{n}}\left( X \right)=\dfrac{1}{1-n} \log_2 \left( \sum\limits_{i=1}^{N}{p_{i}^{n}} \right)$. It then says that the limit as $n\to \infty $ is $-\log_2 \left( p_1 \right)$. I saw another article that uses the m... | information theory entropy | 1 |
6,245 | Is there a data-structure for semilattices similar to a tree data-structure? | <p>If we regard a tree as a partial ordered set, it becomes a special case of a join-semilattice. For a join-semilattice, we want to be able to compute the (unique) least upper bound of two elements (more or less) efficiently. In the case of a tree, a data structure which would enable this would be to store for each el... | data structures lattices | 1 |
6,247 | Do "inductively" and "recursively" have very similar meanings? | <p>Do "inductively" and "recursively" mean very similar?</p>

<p>For example, if there is an algorithm that determines a n-dim vector by determine its first k+1 components based on its first k components having been determined, and is initialized with the first component, would you call it works recursively or ... | algorithms terminology recursion induction | 1 |
6,249 | Constructing a tree from disjoint graphs | <p>I will preface my question with the definition of a simple tree that applies to my question:</p>

<blockquote>
 <p>A simple tree is an undirected and connected graph with no cycles.</p>
</blockquote>

<p>I am having difficulty coming up with a compelling argument that a tree of the above def... | graphs trees | 1 |
6,253 | Visualizing a Non Deterministic Decider | <p>I know that we can visualize a Non deterministic TM as a TM which splits into multiple copies of itself whenever it sees a non deterministic path (Yes, I also know that this is just a visualization and is usually used by beginners like me for understanding non determistisism). </p>

<p>Further, I also know t... | turing machines undecidability nondeterminism | 1 |
6,259 | Assumption on weights in threshold circuits | <p>A threshold gate implementing a linear threshold function on $n$ boolean inputs $x_1, x_2 \ldots, x_n$ is given by the equation:
$w_1 x_1 + w_2 x_2 + \ldots, w_n x_n \ge t$
where $w_1, \ldots, w_n, t \in \mathbb{R}$. The $w_i$'s are called the weights of the threshold function and $t$ is called the threshold... | complexity theory circuits | 1 |
6,262 | If a predicate is not computable, what can be said about its negation? | <p>Doing the following exercise:</p>
<blockquote>
<p>Let <span class="math-container">$\overline{HALT(x,y)}$</span> be defined as</p>
<p><span class="math-container">$\overline {HALT(x,y)} \iff \text{program number y never halts on input x}$</span></p>
<p>Show that it is not computable.</p>
</blockq... | computability proof techniques | 1 |
6,263 | How to prove or disprove that f is computable? | <p>If $f(x_1,\dots, x_n)$ is a total function that for some constant $K$, $f(x_1,\dots, x_n) \leq K$ for all $x_1,\dots, x_n$ then $f$ is computable. </p>

<p>I want some hints on how to prove/disprove the above claim. This an exercise from the book <a href="http://rads.stackoverflow.com/amzn/click/0122063821" ... | computability proof techniques | 1 |
6,266 | Comparing rational numbers | <p>Given $a,b,c,d \in \mathbb N$ and $b,d \notin \{0\}$,</p>

<p>$$
\begin{eqnarray*}
\frac a b < \frac c d &\iff& ad < cb
\end{eqnarray*}
$$</p>

<p>My questions are:</p>

<p>Given $a,b,c,d$</p>

<ol>
<li>Assuming we can decide $x < y \in \mathbb Z$ ... | algorithms integers | 0 |
6,274 | Recurrence relation for time complexity $T(n) = T(n-1) + n^2$ | <p>I'm looking for a $\Theta$ approximation of
$$T(n) = T(n-1) + cn^{2}$$</p>

<p>This is what I have so far:</p>

<p>$$
\begin{align*}
T(n-1)& = T(n-2) + c(n-1)^2\\
T(n) &= T(n-2) + c(n-1) + cn^2\\[1ex]
T(n-2) &= T(n-3) + c(n-2)^2\\
T(n) & = T(n-3) + c(n-2)^2 + c... | time complexity algorithm analysis proof techniques recurrence relation | 1 |
6,276 | Regarding the height of a recursion tree on dynamic programming | <p>I am trying to understand dynamic programming and I am watching this mit video. If you guys could take some time out , can you refer to the slide on 41:36 . Why is the height m+n. I just don't get it why is the heigh of this recurrence tree m+n.</p>

<p><a href="http://videolectures.net/mit6046jf05_leiserson... | recurrence relation dynamic programming | 1 |
6,277 | Why is the minimum height of a binary tree $\log_2(n+1) - 1$? | <p>In my Java class, we are learning about complexity of different types of collections.</p>

<p>Soon we will be discussing binary trees, which I have been reading up on. The book states that the minimum height of a binary tree is $\log_2(n+1) - 1$, but doesn't offer further explanation.</p>

<p>Can som... | data structures binary trees discrete mathematics trees | 1 |
6,279 | If $L$ is a regular language, how to prove $L_1 = \{ uv \mid u \in L, |v| =2 \}$ is also regular? | <blockquote>
 <p>If $L$ is a regular language, prove that the language
 $L_1 = \{ uv \mid u \in L, |v| =2 \}$
 is also regular.</p>
</blockquote>

<p>My idea: $L$ can be represented as a DFA and then you could add 2 consecutive transitions from every final state for the letters of $v$, creati... | regular languages automata finite automata closure properties check my answer | 1 |
6,284 | Instruction Translation | <p>Imagine two machines of different architecture which produce output of a standard format.</p>

<p>If you have a program for one machine and can observe it's operation and output, what techniques exist to automatically produce an equivalent program for the alternate architecture?</p>

<p>By equivalent... | programming languages compilers | 1 |
6,285 | Who conceived the concept of Discrete Event Simulation, and when? | <p>I'm trying to trace back the origin of the general concept of Discrete Event Simulation and found a 1968 article by Fishman and Kiviat mentioning the term. It is titled <em>The statistics of discrete-event simulation</em>.</p>

<p>However, I'm unable to verify this as the origin of the term.</p>

<p>... | reference request simulation history | 0 |
6,288 | Are randomized algorithms constructive? | <p>From , the proofs by the probabilistic method are often said to be non-constructive.</p>

<p>However, a proof by probabilistic method indeed designs a randomized algorithm and uses it for proving existence. Quoted from p103 of <a href="http://books.google.com/books?id=QKVY4mDivBEC&pg=PR5&lpg=PP1&... | algorithms terminology randomized algorithms | 1 |
6,290 | Help need to learn Quantum Computation and Information | <p>I want to learn quantum computation and information. I am studying from Nielsen & Chuang book for this.
Is there any online vedio (lecture series) starts from
basics of quantum computation and information up to factorization, discrete log, search etc? </p>
 | reference request education quantum computing | 1 |
6,291 | Polynomial time reducibility | <blockquote>
 <p>$L_1$ and $L_2$ are two languages defined on the alphabet $\sum$.
 $L_1$ is reducible to $L_2$ in polynomial time. Which of the following
 cannot be true?</p>
 
 <ul>
 <li>$L_1 \in P$ and $L_2$ is finite</li>
 <li>$L_1 \in NP$ and $L_2 \in P$</li>
 <li>$L_1$ is u... | complexity theory reductions complexity classes | 1 |
6,295 | What is the time complexity of computing $\frac{1}{2^n} {{n}\choose{(n+2)/2}}$ | <p>What is the time complexity of computing $\frac{1}{2^n} {{n}\choose{(n+2)/2}}$?</p>

<p>$$\frac{1}{2^n} {{n}\choose{(n+2)/2}} = \frac{1}{2^n} \frac{n(n-1)\cdots ((n-2)/2)}{((n+2)/2) (n/2) \cdots 1}$$</p>

<p>The numerator and denominator in $\frac{n(n-1)\cdots ((n-2)/2)}{((n+2)/2) (n/2) \cdots 1}$ wi... | algorithms time complexity discrete mathematics | 0 |
6,296 | References on comparison between quantum computers and Turing machines | <p>I was told that quantum computers are not computationally more powerful than Turing machines.
Could someone kindly help in giving some literature references explaining that fact?</p>
 | computability reference request turing machines quantum computing | 0 |
6,301 | Adjacent house , dynamic programming problem | <p>I have to be honest this is a homework problem, but I just need to discuss this with some one. The problem is there is a row of n houses, with different profit e.g profit1 for house 1, it can be either positive or negative value. But the aim is to maximize the profit by buying a subset of these houses. So infact, yo... | dynamic programming knapsack problems | 1 |
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