# turing machine Published articles for turing machine. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## The names of birds, part 4 DevFeed: [The names of birds, part 4]() Original publisher: [Read original article]() Author: ericlippert Published: 2023-02-03T17:17:57Z Content type: article Language: en Sources: [Eric Lippert]() Topics: [Math and Logic](), [function](), [functions]() Tags: [computer](), [lambda-calculus](), [logic](), [turing-machine](), [uncategorized]() ### AI overview This article explains combinatory logic through the fictional identities of birds representing the S and K combinators. It shows how these combinators can produce the identity combinator and the duplication combinator, then connects combinatory logic with lambda calculus and computation. ### Source excerpt The European starling is a lovely looking bird, though territorial, noisy and aggressive up close. Unfortunately, they are very invasive in North America. Most of the hundreds of millions of European starlings now living in the Americas can be found ... Continue reading -> ## Other Complexity Classes DevFeed: [Other Complexity Classes]() Original publisher: [Read original article]() Published: 2012-02-29T17:12:35Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Algorithms, Complexity](), [Computing](), [Math and Logic]() Tags: [complexity](), [computational-complexity](), [halting-problem](), [kolmogorov-complexity](), [nondeterminism](), [open-questions](), [oracle](), [primer](), [pspace](), [turing-machine](), [turing-machines]() ### AI overview This article introduces complexity classes beyond P and NP, including PSPACE and NPSPACE, and discusses oracle-based classes. It explains that PSPACE equals NPSPACE while many relationships among complexity classes remain open. ### Source excerpt Not Just Time, But Space Too! So far on this blog we've introduced models for computation, focused on Turing machines and given a short overview of the two most fundamental classes of problems: P and NP. While the most significant open question in the theory of computation is still whether P = NP, it turns out that there are hundreds (almost 500, in fact!) other "classes" of problems whose relationships are more or less unknown. ## 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. ## Busy Beavers, and the Quest for Big Numbers DevFeed: [Busy Beavers, and the Quest for Big Numbers]() Original publisher: [Read original article]() Published: 2012-02-08T19:42:22Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [Math and Logic](), [Computing]() Tags: [ackermann-function](), [busy-beaver](), [chessboard](), [computing](), [infinite](), [mathematics](), [numbers](), [primer](), [theory](), [turing-machine]() ### AI overview This article examines how the ability to describe very large numbers reflects progress in mathematical and scientific thought. It introduces historical examples, including Archimedes' estimate for the number of grains of sand in the universe, and connects them to computational topics such as Busy Beavers. ### Source excerpt Finding Bigger Numbers, a Measure of Human Intellectual Progress Before we get into the nitty gritty mathematics, I'd like to mirror the philosophical and historical insights that one can draw from the study of large numbers. That may seem odd at first. What does one even mean by "studying" a large number? Of course, I don't mean we stare at the number 1,000,000,000,000, which is quite large, and wonder how mankind can benefit from its elusive properties. ## False Proof--All Numbers are Describable in at Most Twenty Words DevFeed: [False Proof--All Numbers are Describable in at Most Twenty Words]() Original publisher: [Read original article]() Published: 2011-07-28T16:03:27Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [Math and Logic](), [Statement]() Tags: [computer](), [false-proof](), [kolmogorov-complexity](), [language](), [mathematics](), [program](), [set-theory](), [turing-machine](), [well-ordering]() ### AI overview The article examines a false proof claiming that every natural number can be described in fewer than twenty words. It explains that the contradiction arises from imprecise notions of description and set construction, connecting the issue to Russell's paradox and the Richard-Berry paradox. ### Source excerpt Problem: Show that every natural number can be unambiguously described in fewer than twenty words. "Solution": Suppose to the contrary that not every natural number can be so described. Let $ S$ be the set of all natural numbers which are describable in fewer than twenty words. Consider $ R = \mathbb{N}-S$, the set of all words which cannot be described in fewer than twenty words. Since $ R$ is a subset of the natural numbers, which is well-ordered, it has a unique smallest element which we call $ r$. ## Turing Machines and Conway's Dreams DevFeed: [Turing Machines and Conway's Dreams]() Original publisher: [Read original article]() Published: 2011-06-30T20:50:04Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Automaton]() Tags: [cellular](), [cellular-automata](), [computability-theory](), [computational-complexity](), [conway](), [infinite](), [life](), [mathematics](), [patterns](), [period](), [programming](), [recursion](), [theory](), [turing-machine](), [turing-machines]() ### AI overview The article examines Conway's Game of Life patterns that do not stabilize, including Gosper's glider gun and puffers that produce continuing activity. It connects these patterns to computability, explaining that infinite looping is necessary for Turing-complete computation. ### Source excerpt Additional Patterns Last time we left the reader with the assertion that Conway's game of life does not always stabilize. Specifically, there exist patterns which result in unbounded cell population growth. Although John Conway's original conjecture was that all patterns eventually stabilize (and offered $50 to anyone who could provide a proof or counterexample), he was proven wrong. Here we have the appropriately named glider gun, whose main body oscillates, expelling a glider once per period. ## Introduction to Cellular Automata DevFeed: [Introduction to Cellular Automata]() Original publisher: [Read original article]() Published: 2011-06-29T21:08:45Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Cellular automaton](), [Automaton](), [Finite-state machine]() Tags: [cellular-automata](), [computability-theory](), [conus](), [conway](), [life](), [mathematica](), [mathematics](), [patterns](), [programming](), [rules](), [simulation](), [turing-machine]() ### AI overview An introductory tutorial on cellular automata, explaining cells, states, transition rules, simultaneous updates, and a one-dimensional binary example. ### Source excerpt Cellular Automata There is a long history of mathematical models for computation. One very important one is the Turing Machine, which is the foundation of our implementations of actual computers today. On the other end of the spectrum, one of the simpler models of computation (often simply called a system) is a cellular automaton. Surprisingly enough, there are deep connections between the two. But before we get ahead of ourselves, let's see what these automata can do.