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Are there any references covering this?	Could you please provide more details about the specific topic or area you are looking for references on? This will help me assist you better!	[ { "from": "human", "value": "Are there any references covering this?\n" }, { "from": "gpt", "value": "Could you please provide more details about the specific topic or area you are looking for references on? This will help me assist you better!" } ]
What are the most significant annual Complexity Theory conferences? Rules: One conference per answer Include a link to the conference	Conference: Annual IEEE Conference on Computational Complexity (CCC) Link: [CCC Conference](https://computationalcomplexity.org/)	[ { "from": "human", "value": "What are the most significant annual Complexity Theory conferences?\nRules:\n\nOne conference per answer\nInclude a link to the conference \n\n" }, { "from": "gpt", "value": "Conference: Annual IEEE Conference on Computational Complexity (CCC) \nLink: [CCC C...
Which algorithms are used most often? Please write a single algorithm per answer, try to keep your answer short (one or two lines).	1. Linear Regression: A statistical method used for predicting the value of a dependent variable based on the value of one or more independent variables.	[ { "from": "human", "value": "\nWhich algorithms are used most often?\n\nPlease write a single algorithm per answer, try to keep your answer short (one or two lines).\n" }, { "from": "gpt", "value": "1. Linear Regression: A statistical method used for predicting the value of a dependent varia...
I was just wondering if this was possible? Surely there maybe some naive methods of doing so, but I was just wondering if someone can suggest efficient ways to do so.	Absolutely! If you provide more context on what specific task or problem you are referring to, I can offer a more tailored response. Whether it’s data processing, algorithm optimization, or something else, there are often both naive and efficient methods to tackle various challenges. Please elaborate on the topic or ta...	[ { "from": "human", "value": "I was just wondering if this was possible?\nSurely there maybe some naive methods of doing so, but I was just wondering if someone can suggest efficient ways to do so.\n" }, { "from": "gpt", "value": "Absolutely! If you provide more context on what specific task or p...
What is the funniest TCS-related published work you know? Please include only those that are intended to be funny. Works which are explicitly crafted to be intelligently humorous (rather than, say, a published collection of short jokes regarding complexity theory) are preferred. Works with humorous (actually humorous...	One of the funniest TCS-related works is "The Complexity of Theorem Proving Procedures" by Stephen A. Cook, which is a playful take on the formalism of complexity theory, presenting serious concepts with a humorous twist that makes light of the often dry and intricate nature of the subject. Its title alone offers a sly...	[ { "from": "human", "value": "What is the funniest TCS-related published work you know?\nPlease include only those that are intended to be funny. Works which are explicitly crafted to be intelligently humorous (rather than, say, a published collection of short jokes regarding complexity theory) are preferre...
What is the exact time complexity of the undirected st-connectivity log-space algorithm by Omer Reingold ?	Omer Reingold's algorithm for undirected st-connectivity in logarithmic space has a time complexity of \( O(n^{2}) \), where \( n \) is the number of vertices in the graph. The algorithm makes use of a technique called "interactive proofs," which combines ideas from graph theory and complexity theory. To summarize, th...	[ { "from": "human", "value": "What is the exact time complexity of the undirected st-connectivity log-space algorithm by Omer Reingold ?\n" }, { "from": "gpt", "value": "Omer Reingold's algorithm for undirected st-connectivity in logarithmic space has a time complexity of \\( O(n^{2}) \\), where ...
The standard proof of the Chernoff bound (from the Randomized Algorithms textbook) uses the Markov inequality and moment generating functions, with a bit of a Taylor expansion thrown in. Nothing too difficult, but somewhat mechanical. But there are other Chernoff bound proofs that expose the deeper structure driving t...	Example: The Central Limit Theorem (CLT) Textbook Proof: The standard proof of the Central Limit Theorem often uses characteristic functions (or moment generating functions) along with the continuity theorem. This approach typically starts from the definition of the sum of independent random variables and show...	[ { "from": "human", "value": "The standard proof of the Chernoff bound (from the Randomized Algorithms textbook) uses the Markov inequality and moment generating functions, with a bit of a Taylor expansion thrown in. Nothing too difficult, but somewhat mechanical. \nBut there are other Chernoff bound proofs ...
Two papers I would include are: D. Kozen, "Indexing of subrecursive classes", STOC, 1978. R. Ladner, "On the Structure of Polynomial Time Reducibility", JACM, 1975.	Those are both important papers in the field of computational complexity theory and subrecursive functions. Here’s a brief overview of each paper: 1. D. Kozen, "Indexing of subrecursive classes", STOC, 1978: - This paper discusses the classification and indexing of subrecursive function classes, which are funda...	[ { "from": "human", "value": "Two papers I would include are:\n\nD. Kozen, \"Indexing of subrecursive classes\", STOC, 1978.\nR. Ladner, \"On the Structure of Polynomial Time Reducibility\", JACM, 1975.\n\n" }, { "from": "gpt", "value": "Those are both important papers in the field of computation...
I'm often asked what a theoretical computer scientist does. It would be great to have some nice responses to this question. I tend to fall back to technical jargon and people's eyes usually glaze over at this point. What does a theoretical computer scientist do, in terms that can be understood by people who are not ...	A theoretical computer scientist is like a puzzle solver who explores the fundamental principles of what computers can do and how they can do it efficiently. They ask questions like, "What problems can we solve with computers?" and "How fast can we solve them?" By understanding the limits and capabilities of computatio...	[ { "from": "human", "value": "I'm often asked what a theoretical computer scientist does. It would be great to have some nice responses to this question. I tend to fall back to technical jargon and people's eyes usually glaze over at this point.\n\nWhat does a theoretical computer scientist do, in terms th...
Where can I get the photo of “Introduction to automata theory, languages and computation” by Hopcroft and Ullman '79 (first edition) cover in order to be able to read all the phrases placed on the cover? Obviously the ones that gave me Google.Images (from Wikipedia, Amazon and others) do not allow this. Solved: http://...	It looks like you've already found a suitable link to the cover of "Introduction to Automata Theory, Languages, and Computation" by Hopcroft and Ullman. If you're looking for high-resolution images or specific phrases, you may also consider checking academic library databases, online retailers, or archives of universit...	[ { "from": "human", "value": "Where can I get the photo of “Introduction to automata theory, languages and computation” by Hopcroft and Ullman '79 (first edition) cover in order to be able to read all the phrases placed on the cover? Obviously the ones that gave me Google.Images (from Wikipedia, Amazon and o...
I have been working on this thread Grid $k$-coloring without monochromatic rectangles, and I am aware that the four color theorem implies that all planar graphs are four colorable. The question is whether this is a necessary condition as well, i.e. whether having a proof that a graph is not planar implies it is not fo...	No, having a proof that a graph is not planar does not imply that it is not four colorable. The four color theorem states that every planar graph can be colored with at most four colors such that no two adjacent vertices share the same color. However, this theorem does not extend to non-planar graphs, which means that ...	[ { "from": "human", "value": "I have been working on this thread Grid $k$-coloring without monochromatic rectangles, and I am aware that the four color theorem implies that all planar graphs are four colorable. \nThe question is whether this is a necessary condition as well, i.e. whether having a proof that ...
Can someone please summarize the exact difference between NP-Complete and NP-Hard problems in simple language? Wiki and my standard books aren't exactly helping.	Sure! Let's break it down simply: NP (Nondeterministic Polynomial time) is a class of problems for which a solution can be checked quickly (in polynomial time) if you are given a solution. NP-Complete problems are a subset of NP problems that are the hardest among NP problems. If you can find a fast solution...	[ { "from": "human", "value": "Can someone please summarize the exact difference between NP-Complete and NP-Hard problems in simple language? Wiki and my standard books aren't exactly helping.\n" }, { "from": "gpt", "value": "Sure! Let's break it down simply:\n\n**NP (Nondeterministic Polynomial t...
First of all I am of course aware of the wikipedia article: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem However I still do not understand exactly what the problem is. To demonstrate that I've tried, I think it is as follows but I am not sure: The problem of checking whether a given boolean equation wit...	Yes, you are on the right track! The Boolean Satisfiability Problem (SAT) is indeed about determining whether a given Boolean formula can be satisfied by some assignment of truth values (true or false) to its variables. In other words, you want to check if there exists a way to assign truth values to the variables such...	[ { "from": "human", "value": "First of all I am of course aware of the wikipedia article: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem\nHowever I still do not understand exactly what the problem is. To demonstrate that I've tried, I think it is as follows but I am not sure:\n\nThe problem of c...
I would like to ask, if anybody knows, whether there exists a 3-regular bridgeless graph which does not have a hamiltonian path (not necessarily extended to a hamiltonian circuit). Thank you	Yes, there exist 3-regular (cubic) bridgeless graphs that do not have a Hamiltonian path. A classic example of such a graph is the Petersen graph. The Petersen graph is a well-known cubic graph that is bridgeless, meaning it does not contain any bridges (edges whose removal would increase the number of connected co...	[ { "from": "human", "value": "I would like to ask, if anybody knows, whether there exists a 3-regular bridgeless graph which does not have a hamiltonian path (not necessarily extended to a hamiltonian circuit). Thank you\n" }, { "from": "gpt", "value": "Yes, there exist 3-regular (cubic) bridgele...
It is known that generic k-SAT formulas may exhibit the presence of exponentially many solution clusters. Question: Is it true also for Monotone-2SAT formulas? For the definition of cluster, see Kaveh's answer to the question SAT Solution Space - Definition of Cluster of Solutions.	In the context of SAT problems, particularly Monotone-2SAT (where each clause contains exactly two literals and no negated literals), the presence of clusters of solutions is indeed a relevant topic. For generic k-SAT problems, it has been observed that as the number of variables increases, the solution space can dis...	[ { "from": "human", "value": "It is known that generic k-SAT formulas may exhibit the presence of exponentially many solution clusters.\n\nQuestion:\nIs it true also for Monotone-2SAT formulas?\n\nFor the definition of cluster, see Kaveh's answer to the question SAT Solution Space - Definition of Cluster of ...
A star system is a family $F$ of n subsets of n-elements set $S$. A star system is graphical if there is some graph $G(V,E)$ such that $F$ is the family of vertex neighborhoods in $G$. It is $NP$-complete to decide whether a given star system is graphical. What is the minimum occurrence of each element such that the p...	The problem of determining whether a given star system is graphical is indeed NP-complete. Regarding your first question about the minimum occurrence of each element in the star system, the result shows that each element must occur in at least two subsets. This is because if an element appears in only one subset, it ca...	[ { "from": "human", "value": "A star system is a family $F$ of n subsets of n-elements set $S$. A star system is graphical if there is some graph $G(V,E)$ such that $F$ is the family of vertex neighborhoods in $G$. It is $NP$-complete to decide whether a given star system is graphical.\n\nWhat is the minimum...
It is known that determining whether or not a given triangulated 3-manifold is a 3-sphere is in NP, via work by Saul Schleimer in 2004: "Sphere recognition lies in NP" arXiv:math/0407047v1 [math.GT]. I am wondering if this has been established to be NP-complete in the last five or six years? Analogous problems, such as...	As of my last update in October 2023, the problem of determining whether a given triangulated 3-manifold is a 3-sphere is known to be in NP, as established by Saul Schleimer in his 2004 paper. However, it has not been established as NP-complete. The distinction between being in NP and being NP-complete is significant....	[ { "from": "human", "value": "It is known that determining whether or not a given triangulated 3-manifold is a 3-sphere\nis in NP, via work by\nSaul Schleimer in 2004: \"Sphere recognition lies in NP\"\narXiv:math/0407047v1 [math.GT].\nI am wondering if this has been established to be NP-complete in the last...
In 1995, Russell Impagliazzo proposed five complexity worlds: 1- Algorithmica: $P=NP$ with all the amazing consequences. 2- Heuristica: $NP$-complete problems are hard in the worst-case ($P \ne NP$) but are efficiently solvable in the average-case. 3- Pessiland: There exist average-case $NP$-complete problems but one-w...	In recent years, the predominant sentiment in the field of computational complexity suggests that the world of Pessiland is increasingly favored. This perspective stems from various advances and results in both average-case complexity and cryptography, which seem to indicate limitations on the hardness of NP-comple...	[ { "from": "human", "value": "In 1995, Russell Impagliazzo proposed five complexity worlds:\n1- Algorithmica: $P=NP$ with all the amazing consequences.\n2- Heuristica: $NP$-complete problems are hard in the worst-case ($P \\ne NP$) but are efficiently solvable in the average-case.\n3- Pessiland: There exist ...
The sign rank of a matrix A with +1,-1 entries is the least rank (over the reals) of a matrix B which has the same sign pattern as A (i.e., $A_{ij}B_{ij}>0$ for all $i,j$). This notion is important in communication complexity and learning theory. My question is: Are there any known (subexponential time) algorithms that...	As of my last knowledge update in October 2023, there are no known algorithms that can approximate the sign-rank of a matrix to within a factor of \(o(n)\) in subexponential time. The challenge in approximating the sign-rank stems from its relation to various complexity-theoretic problems and the difficulty of determin...	[ { "from": "human", "value": "The sign rank of a matrix A with +1,-1 entries is the least rank (over the reals) of a matrix B which has the same sign pattern as A (i.e., $A_{ij}B_{ij}>0$ for all $i,j$). This notion is important in communication complexity and learning theory.\nMy question is: Are there any k...
In a 2006 presentation titled EXPANDER GRAPHS - ARE THERE ANY MYSTERIES LEFT? , Nati Linial posed the following open problem: Which $NP$-hard computational problem on graph remain hard when restricted to expander graphs? Since then, Has any progress been made to prove such result for an $NP$-hard problem?	As of my last knowledge update in October 2023, there has been ongoing research into the complexity of various NP-hard problems restricted to special classes of graphs, including expander graphs. While some NP-hard problems have been shown to remain NP-hard even when restricted to certain families of graphs, there has ...	[ { "from": "human", "value": "In a 2006 presentation titled EXPANDER GRAPHS - ARE THERE ANY MYSTERIES LEFT? \n, Nati Linial posed the following open problem:\n\nWhich $NP$-hard computational problem on graph remain hard when restricted to expander graphs?\n\nSince then, Has any progress been made to prove s...
Coppersmith–Winograd algorithm is the asymptotically fastest known algorithm for multiplying two $n \times n$ square matrices. The running time of their algorithm is $O(n^{2.376})$ which is the best known so far. What is the space complexity of this algorithm ? Is it in $\Theta(n^2)$ ?	The Coppersmith–Winograd algorithm is known for its asymptotic time complexity of \( O(n^{2.376}) \) for multiplying two \( n \times n \) matrices. Regarding space complexity, the Coppersmith–Winograd algorithm and its variations typically require space to store the matrices being multiplied and any additional data str...	[ { "from": "human", "value": "Coppersmith–Winograd algorithm is the asymptotically fastest known algorithm for multiplying two $n \\times n$ square matrices. The running time of their algorithm is $O(n^{2.376})$ which is the best known so far. What is the space complexity of this algorithm ? Is it in $\\The...
It is easy to look in a lot of textbooks the proofs of subject reduction and strong normalisation for System F, also, sometimes there are definitions of System F with pairs, where (t,r) is a term, not only an encoding. The question is, what would be the reference for this system?	System F, also known as the polymorphic lambda calculus, was introduced by Jean-Yves Girard in his 1972 paper "Interprétation fonctionnelle et élimination des coupures," and its study has been extensively documented in the literature. The extension of System F to include pairs as first-class terms rather than just enc...	[ { "from": "human", "value": "It is easy to look in a lot of textbooks the proofs of subject reduction and strong normalisation for System F, also, sometimes there are definitions of System F with pairs, where (t,r) is a term, not only an encoding. The question is, what would be the reference for this system...
A Quine is a computer program which produces a copy of its own source code as its only output. Is there any Quine program that could print itself out n times, with n specified some way in the program?	Yes, it is possible to create a Quine that prints itself out `n` times, where `n` is specified in the program itself. Below is an example of such a Quine written in Python: ```python n = 5 # Change this value to print the Quine n times quine = '''n = {n} # Change this value to print the Quine n times quine = {0}{1}{...	[ { "from": "human", "value": "A Quine is a computer program which produces a copy of its own source code as its only output. Is there any Quine program that could print itself out n times, with n specified some way in the program?\n" }, { "from": "gpt", "value": "Yes, it is possible to create a Q...
In Purely Functional Worst Case Constant Time Catenable Sorted Lists, Brodal et al. present purely functional balanced trees with O(1) concatenate and O(lg n) insert, delete, and find. The data structure is somewhat complicated. Is there a simpler balanced search tree with O(1) concatenate, functional or not?	Yes, there is a simpler approach to creating a balanced search tree that supports O(1) concatenation operations. One such data structure is the finger tree. Finger trees are a versatile data structure that can be implemented to support various operations efficiently, including concatenation. Finger trees maintain ...	[ { "from": "human", "value": "In Purely Functional Worst Case Constant Time Catenable Sorted Lists, Brodal et al. present purely functional balanced trees with O(1) concatenate and O(lg n) insert, delete, and find. The data structure is somewhat complicated.\nIs there a simpler balanced search tree with O(1)...
It is well known that the NP-Complete Problem called Subset Sum has a FPTAS. I was wondering if there existed an PSPACE Complete problem which also has a FPTAS? Thanks in advance.	The question of whether there exists a PSPACE-complete problem that also has a Fully Polynomial-Time Approximation Scheme (FPTAS) is an interesting one. To clarify, an FPTAS is an algorithm that, for any given ε > 0, produces a solution that is within a factor of (1 - ε) of the optimal solution in polynomial time wit...	[ { "from": "human", "value": "It is well known that the NP-Complete Problem called Subset Sum has a FPTAS. I was wondering if there existed an PSPACE Complete problem which also has a FPTAS? Thanks in advance.\n" }, { "from": "gpt", "value": "The question of whether there exists a PSPACE-complete...
What are the best current lower bounds for time and circuit depth for 3SAT?	As of my last knowledge update in October 2023, the best-known lower bounds for the time complexity and circuit depth of 3SAT largely stem from results in the context of NP-completeness and circuit complexity. 1. Time Complexity: 3SAT is NP-complete, meaning that no polynomial-time algorithm is known for solving i...	[ { "from": "human", "value": "What are the best current lower bounds for time and circuit depth for 3SAT?\n" }, { "from": "gpt", "value": "As of my last knowledge update in October 2023, the best-known lower bounds for the time complexity and circuit depth of 3SAT largely stem from results in the...
In the thread Major unsolved problems in theoretical computer science?, Iddo Tzameret made the following excellent comment: I think we should distinguish between major open problems that are viewed as fundamental problems, like $ P\neq NP $, and major open problems which will constitute a technical breakthrough, if s...	One example of a problem that sits at the frontier of theoretical computer science is: Problem: Prove exponential lower bounds for $AC^0[6]$ circuits. Explanation: The class $AC^0$ consists of families of circuits that are of constant depth and have unbounded fan-in AND, OR, and NOT gates. The question of whe...	[ { "from": "human", "value": "In the thread Major unsolved problems in theoretical computer science?, Iddo Tzameret made the following excellent comment:\n\nI think we should distinguish between major open problems that are viewed as fundamental problems, like $ P\\neq NP $, and major open problems which wi...
What should you do when you see a question raised in public, say here on stack-exchange, that you know the answer to, because you are looking into as part of current research project? For example, I see a TCS.SX question that I know the answer to, because I worked on the problem recently. I haven't finished writing up...	When you come across a question on a platform like Stack Exchange that you know the answer to due to your current research, you have a few options to consider. Here's a suggested approach: 1. Check for Disclosure and Timing: If your results are not yet published or you haven't communicated them in a public forum, ...	[ { "from": "human", "value": "What should you do when you see a question raised in public, say here on stack-exchange, that you know the answer to, because you are looking into as part of current research project?\nFor example, I see a TCS.SX question that I know the answer to, because I worked on the proble...
Natural proofs is a barrier towards proving lower bounds on the circuit complexity of boolean functions. They do not directly imply any such barrier in proving lower bounds on the $monotone$ circuit complexity. Is there any progress towards identifying such barriers ? Are there other barriers in the monotone setting ?	The concept of "natural proofs," introduced by Razborov and Rudich in the context of circuit complexity, establishes certain limitations on proving lower bounds for general circuit classes. Natural proofs leverage certain properties (like being efficient to verify and being "natural") and have been shown to be incompat...	[ { "from": "human", "value": "Natural proofs is a barrier towards proving lower bounds on the circuit complexity of boolean functions. They do not directly imply any such barrier in proving lower bounds on the $monotone$ circuit complexity. Is there any progress towards identifying such barriers ? Are there ...
I've been reading Nielson & Nielson's "Semantics with Applications", and I really like the subject. I'd like to have one more book on programming language semantics -- but I really can get only one. I took a look at the Turbak/Gifford book, but it's too long-winded; I thought Winskel would be fine, but I have no access...	Winskel's "The Formal Semantics of Programming Languages" is indeed a well-regarded text in the field of programming language semantics. It provides a solid introduction to the topic and focuses on denotational semantics, operational semantics, and algebraic semantics, among other approaches. While it was published in ...	[ { "from": "human", "value": "I've been reading Nielson & Nielson's \"Semantics with Applications\", and I really like the subject. I'd like to have one more book on programming language semantics -- but I really can get only one.\nI took a look at the Turbak/Gifford book, but it's too long-winded; I thought...
Immerman and Szelepcsenyi independently proved that $NL=coNL$. Using their technique of inductive counting, Borodin et al proved that $SAC^i$ is closed under complementation, for $i > 0$. Prior to Reingold's theorem ($SL=L$), Nisan and Ta-Shma proved $SL=coSL$, using logspace uniform projection reductions. A 1996 paper...	As of my last knowledge update in October 2023, the original proofs of \( NL = coNL \) by Immerman and Szelepcsenyi, along with the proof using inductive counting by Borodin et al., remain the most prominent techniques known for establishing this equality in complexity theory. The request for a proof using techniques s...	[ { "from": "human", "value": "Immerman and Szelepcsenyi independently proved that $NL=coNL$. Using their technique of inductive counting, Borodin et al proved that $SAC^i$ is closed under complementation, for $i > 0$. Prior to Reingold's theorem ($SL=L$), Nisan and Ta-Shma proved $SL=coSL$, using logspace un...
I am familiar with the theorem which states that some languages are not in the RE (Recursively Enumerable) class of languages, but that can mean either that they are all in CO-RE (or rather, the part of it that doesn't intersect with RE), or that they are partly in CO-RE and partly somewhere else. Are there languages ...	Yes, there are indeed languages for which it is undecidable whether a given word belongs to the language or not, meaning that we cannot even determine whether a word is not in the language. This phenomenon occurs within the realm of computation and formal language theory, and it relates to the concepts of recursively e...	[ { "from": "human", "value": "I am familiar with the theorem which states that some languages are not in the RE (Recursively Enumerable) class of languages, but that can mean either that they are all in CO-RE (or rather, the part of it that doesn't intersect with RE), or that they are partly in CO-RE and par...
In the paper "A Compendium of Problems Complete for P" by Greenlaw, Hoover and Ruzzo (PS) (PDF), there is a list of problems in P that are not known to be in NC and not known to be P-complete either. (This list subsumes all the open problems in the excellent survey by Karp and Ramachandran.) The open problems list star...	The paper "A Compendium of Problems Complete for P" by Greenlaw, Hoover, and Ruzzo does indeed compile a list of problems in P that are not known to be NC or P-complete. Since that publication, several of these problems have been investigated further, but the number of resolved problems (i.e., proven to be either P-com...	[ { "from": "human", "value": "In the paper \"A Compendium of Problems Complete for P\" by Greenlaw, Hoover and Ruzzo (PS) (PDF), there is a list of problems in P that are not known to be in NC and not known to be P-complete either. (This list subsumes all the open problems in the excellent survey by Karp and...
With some randomized algorithms you can derandomize the algorithm, removing (at a possible cost in run time) the use of random bits and maximizing some lower bound on the objective (usually computed using the fact that the theorems are about the expected performance of the random algorithm). Is there an equivalent for ...	Yes, there are concepts in quantum computing that resemble the idea of "dequantization" as you describe it for randomized algorithms. While the techniques and principles differ due to the nature of quantum mechanics, there have been efforts to analyze and potentially convert quantum algorithms into classical ones, albe...	[ { "from": "human", "value": "With some randomized algorithms you can derandomize the algorithm, removing (at a possible cost in run time) the use of random bits and maximizing some lower bound on the objective (usually computed using the fact that the theorems are about the expected performance of the rando...
A linear PRAM model is a PRAM model without bit operations and at least one operand of the $\times$ instruction is a constant. If in addition we require that the running time does not depend on the bit length of the input then the resulting model is called the arithmetic linear PRAM model. This 1999 paper (ps file) of ...	As of my last knowledge update in October 2023, no widely recognized example has been found that falls within the linear PRAM model but not in the arithmetic linear PRAM model, despite the discussions and explorations in the area of parallel algorithms and models of computation. The difference between these models pr...	[ { "from": "human", "value": "A linear PRAM model is a PRAM model without bit operations and at least one operand of the $\\times$ instruction is a constant. If in addition we require that the running time does not depend on the bit length of the input then the resulting model is called the arithmetic linear...
Does it have anything to do with the heap data structure, for example the Buddy blocks implementation, or does it only take the literal English meaning of the word (a big pile)? I know heap memory is more practical than theoretical, but there's no Stack Exchange for "Practical Computer Science" yet.	The term "heap" in computer science does have multiple meanings depending on the context. Let's clarify both aspects: 1. Heap Data Structure: In this context, a heap is a specialized tree-based data structure that satisfies the heap property. In a max-heap, for example, the parent nodes are always greater than or ...	[ { "from": "human", "value": "Does it have anything to do with the heap data structure, for example the Buddy blocks implementation, or does it only take the literal English meaning of the word (a big pile)?\nI know heap memory is more practical than theoretical, but there's no Stack Exchange for \"Practical...
Is the following a valid algorithm for finding a minimum spanning tree? Given a weighted graph with unique weights, remove the all edges that are the highest cost edge in any cycle of the original full graph. Edit: I've changed the description to draw more attention to the differences between this an Kruskal's algori...	The algorithm you've described is not a valid algorithm for finding a minimum spanning tree (MST) of a graph, even though it has some similarities to cycle-based methods used in certain MST algorithms. Here's a breakdown of why the algorithm fails: 1. Cycle Removal: The process of removing the highest cost edge i...	[ { "from": "human", "value": "Is the following a valid algorithm for finding a minimum spanning tree?\n\nGiven a weighted graph with unique weights, remove the all edges that are the highest cost edge in any cycle of the original full graph.\n\nEdit: I've changed the description to draw more attention to the...
During the introductory computer organization class I recently took, the professor described the limitations of seek time in reading or writing to the disk. He suggested a solution whereby the operating system would prioritize the process whose sectors were then closest to the head. In that case, it could move smoothly...	The concept your professor described relates to disk scheduling algorithms, which are critical in managing how data is read from or written to the disk to optimize performance, particularly with respect to seek time and rotational latency. The idea of prioritizing disk access based on the proximity of the data to the ...	[ { "from": "human", "value": "During the introductory computer organization class I recently took, the professor described the limitations of seek time in reading or writing to the disk. He suggested a solution whereby the operating system would prioritize the process whose sectors were then closest to the h...
I just finished Albert-László Barabási's popular science book "Bursts: The Hidden Pattern Behind Everything We Do" which describes the Lévy flight as an ideal strategy for finding scarce resources in an environment. I immediately wondered whether anyone had studied them as a search algorithm. I could imagine them being...	Yes, Lévy flights have indeed been studied as search algorithms, particularly in the context of optimization problems and pathfinding in various environments. The concept of Lévy flights is derived from the behavior of certain animals and the statistical patterns observed in their search processes. In a computational c...	[ { "from": "human", "value": "I just finished Albert-László Barabási's popular science book \"Bursts: The Hidden Pattern Behind Everything We Do\" which describes the Lévy flight as an ideal strategy for finding scarce resources in an environment. I immediately wondered whether anyone had studied them as a s...
attempt to restate question From the feedback, it is obvious that I have not clearly articulated my point. Also, it is not my intent to be condescending. I very clearly have a notion / idea / question that is contrary to the doctrine subscribed to by the readers of this question. I am genuinely trying to reconcile s...	Your original question seems to revolve around the fundamental significance of the result that the Boolean function PARITY does not lie in \( AC^0 \). To clarify and restate it succinctly: Why is it considered fundamentally important that the PARITY function cannot be computed by circuits of bounded depth and polynomi...	[ { "from": "human", "value": "attempt to restate question\nFrom the feedback, it is obvious that I have not clearly articulated my point. Also, it is not my intent to be condescending. I very clearly have a notion / idea / question that is contrary to the doctrine subscribed to by the readers of this quest...