# np-completeness Published articles for np-completeness. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## NP-hard does not mean hard DevFeed: [NP-hard does not mean hard]() Original publisher: [Read original article]() Published: 2017-12-29T13:30:23Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Algorithms, Complexity](), [Algorithms](), [Programming]() Tags: [algorithm](), [algorithms](), [boolean](), [completeness](), [complexity-theory](), [logic](), [mario](), [mathematics](), [np-completeness](), [np-hard](), [problems](), [real-world](), [regular-languages](), [solve](), [time]() ### AI overview This article explains that NP-hardness is a worst-case mathematical property, not a claim that a problem is always difficult for humans or algorithms. Using Super Mario as an example, it shows how game levels can encode boolean logic and why solving the game in full generality would encompass hard computational problems, while ordinary real-world levels may still be solvable efficiently. ### Source excerpt When NP-hardness pops up on the internet, say because some silly blogger wants to write about video games, it's often tempting to conclude that the problem being proved NP-hard is actually very hard! "Scientists proved Super Mario is NP-hard? I always knew there was a reason I wasn't very good at it!" Sorry, these two are unrelated. NP-hardness means hard in a narrow sense this post should hopefully make clear. After that, we'll explore what "hard" means in a mathematical sense that you can apply beyond NP-hardness to inform your work as a programmer. ## A problem that is not (properly) PAC-learnable DevFeed: [A problem that is not (properly) PAC-learnable]() Original publisher: [Read original article]() Published: 2014-04-21T10:00:16Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Learning](), [math](), [Math and Logic]() Tags: [algorithm](), [boolean](), [boolean-satisfiability](), [classes](), [computational-complexity](), [computational-learning-theory](), [learning-theory](), [logical](), [math](), [mathematics](), [misconceptions](), [np](), [np-completeness](), [pac-learning](), [reduction](), [rp]() ### AI overview This technical learning-theory article presents a standard example of a problem that is not learnable under the previously introduced PAC model, then explains how a more expressive hypothesis class changes that result. Its addendum clarifies that 3-term DNF formulas are not shown to be unlearnable under the standard PAC definition, only under the earlier restricted definition. ### Source excerpt In a previous post we introduced a learning model called Probably Approximately Correct (PAC). We saw an example of a concept class that was easy to learn: intervals on the real line (and more generally, if you did the exercise, axis-aligned rectangles in a fixed dimension). One of the primary goals of studying models of learning is to figure out what is learnable and what is not learnable in the various models. ## How theoretical computer science explains the complexity of puzzle games DevFeed: [How theoretical computer science explains the complexity of puzzle games]() Original publisher: [Read original article]() Published: 2014-03-17T10:00:55Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [computational complexity](), [Algorithms, Complexity](), [Computer science](), [Algorithms](), [Mazes]() Tags: [algorithm](), [art-gallery-problem](), [bin-packing](), [board-games](), [computational-complexity](), [computer](), [computer-science](), [exp](), [game](), [games](), [games-on-graphs](), [graph-coloring](), [greedy-spiders](), [mario](), [nintendo](), [np](), [np-completeness](), [np-hard](), [pancake-flipping](), [pspace](), [puzzle](), [science](), [starcraft](), [video-games]() ### AI overview The article explains that NP-hardness in games describes worst-case computational complexity, not how difficult a game is for human players. It uses examples including Pokémon, Super Mario Bros., Candy Crush Saga, Pac-Man, Doom, Starcraft, Tetris, chess, checkers, and Go to discuss hardness results and practical algorithms. ### Source excerpt Two years ago, Erik Demaine and three other researchers published a fun paper to the arXiv proving that most incarnations of classic nintendo games are NP-hard. This includes almost every Super Mario Brothers, Donkey Kong, and Pokemon title. Back then I wrote a blog post summarizing the technical aspects of their work, and even gave a talk on it to a room full of curious undergraduate math majors. But while bad tech-writers tend to interpret NP-hard as "really really hard," the truth is more complicated. ## Anti-Coordination Games and Stable Graph Colorings DevFeed: [Anti-Coordination Games and Stable Graph Colorings]() Original publisher: [Read original article]() Published: 2013-09-09T09:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Graphs](), [graph theory](), [math]() Tags: [announce](), [anti-coordination](), [game-theory](), [games-on-graphs](), [graph](), [graph-coloring](), [graph-theory](), [network](), [np-completeness](), [paper](), [publication](), [research]() ### AI overview The author announces that a first paper on anti-coordination games and stable colorings has been accepted for publication. The article introduces the problem for a general audience, explaining how graph-based friendship networks affect interactions and raising questions about stability, convergence, centralized strategies, and computational difficulty. ### Source excerpt My First Paper I'm pleased to announce that my first paper, titled "Anti-Coordination Games and Stable Colorings," has been accepted for publication! The venue is the Symposium on Algorithmic Game Theory, which will take place in Aachen, Germany this October. A professor of mine once told me that everyone puts their first few publications on a pedestal, so I'll do my best to keep things down to earth by focusing on the contents of the paper and not my swirling cocktail of pride. ## Classic Nintendo Games are NP-Hard DevFeed: [Classic Nintendo Games are NP-Hard]() Original publisher: [Read original article]() Published: 2012-03-22T18:34:56Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [Math and Logic](), [Computer science](), [infoarena]() Tags: [complexity](), [computational-complexity](), [computer-science](), [donkey-kong](), [games](), [mario](), [mathematics](), [metroid](), [np-completeness](), [np-hard](), [paper](), [pokemon](), [video-games](), [zelda]() ### AI overview The article explains research showing that generalized versions of several classic Nintendo games, including Mario Brothers, Metroid, Donkey Kong, Pokemon, and The Legend of Zelda, are NP-hard. Some are also classified as NP-complete or PSPACE-complete. It outlines reductions from 3-SAT using game-level gadgets for variables and clauses. ### Source excerpt Problem: Prove that generalized versions of Mario Brothers, Metroid, Donkey Kong, Pokemon, and Legend of Zelda are NP-hard. Solution: http://arxiv.org/abs/1203.1895v1 Discussion: Three researchers (including Erik Demaine, a computer science professor at MIT famous for his work with the mathematics of origami) recently finished a paper giving the complexity of a number of classic Nintendo games (the ones I loved to play). All are proven NP-hard, some are shown to be NP-complete, and some are PSPACE-complete. ## P vs. NP, A Primer (And a Proof Written in Racket) DevFeed: [P vs. NP, A Primer (And a Proof Written in Racket)]() Original publisher: [Read original article]() Published: 2012-02-23T19:57:35Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Computing](), [Algorithms, Complexity](), [Racket](), [Programming]() Tags: [algorithm](), [algorithms](), [analysis](), [big-o-notation](), [class](), [computational-complexity](), [computing](), [decidability](), [efficiency](), [fast](), [halting-problem](), [input](), [language](), [machine](), [np-completeness](), [p-versus-np](), [primer](), [racket](), [solve](), [theory](), [turing-machine](), [turing-machines]() ### AI overview A primer on the distinction between decidability and computational efficiency, introducing the complexity class P and its definition in terms of polynomial-time decision by a Turing machine. It also discusses efficient algorithms and gives a card-sorting example. ### Source excerpt Decidability Versus Efficiency In the early days of computing theory, the important questions were primarily about decidability. What sorts of problems are beyond the power of a Turing machine to solve? As we saw in our last primer on Turing machines, the halting problem is such an example: it can never be solved a finite amount of time by a Turing machine. However, more recently (in the past half-century) the focus of computing theory has shifted away from possibility in favor of determining feasibility.