67 Sentences With "checkable" | Random Sentence Generator

I want everything in the mod to be fact checkable.

The first step, Canby explained, was to underline all checkable facts.

And of his material that was checkable, no significant red flags emerged.

And yet, the most fact-checkable president in history stumps even the fact-checkers.

There's a lot of noisy crap on the internet, but also a lot of stuff that is easily checkable.

When my dyslexic mind mangles a word so much that it's rendered un-spell-checkable, I'll deploy an arsenal of workarounds.

"P" problems are solvable in polynomial time; "NP" problems might be solvable in polynomial time, and are checkable in polynomial time.

Moderators curate up-to-date lists of these successes, some of which link back to their authors, making them somewhat checkable.

This niche task was chosen to be easy for a quantum computer while still being checkable—just—by a classical one.

That the sender doesn't know this easily checkable fact indicates he or she is perhaps getting news from a source other than CNN or MSNBC.

For a journalist accustomed to working within the tight box of checkable facts, constructing a narrative from the pure productions of my imagination was liberation itself.

" One evening, Zuker noticed that Trump had tweeted about The Apprentice, claiming that it had been the number one show of the night — "an easily checkable fact.

It's easy to make fun of Trump for not telling the truth about something so easily checkable as the ratings for his State of the union speech.

Now, the brand offers eight different construction options of wheel-able luggage including two sizes of carry-on and checkable luggage, a kids' size, and both carry-on sizes with an outside pocket.

Whenever I travel for work, I constantly take photos with my Pixel 2 cellphone that might seem like irrelevant details but that offer fact-checkable color in greater detail than I could ever write down in a notepad.

While The Get Down never promised to be a fact-checkable historical documentary—it has not been spared criticism for its chronological inconsistencies—the series passes up an opportunity to demonstrate the integration of immigrants as a process of acculturation rather than assimilation.

Or we could be passing around the same handful of un-fact-checkable reports from a group that could secure lucrative consulting deals if Smith decides to roll its services into his business, basically doing pro bono PR work for a small defense consultancy.

The same goes for the murder rate: Mr Trump said something wildly wrong about something easily checkable, leaving an adviser, Kellyanne Conway, flailing to cover for him by saying that Mr Trump may have been "relying on data perhaps for a particular area; I don't know who gave him that data".

Whether attacking his detractors in demeaning terms that would make a bratty 10-year-old cringe or spewing easily checkable lies or capitalizing letters so it feels like a really noisy and angry old man is shaking his fist at the internet 24/7/365, Trump has been one of the major influences on the Twitter platform that has helped make it a cesspool and encouraged others to makes it even dirtier still.

The theory of probabilistically checkable proofs studies the power of probabilistically checkable proof systems under various restrictions of the parameters (completeness, soundness, randomness complexity, query complexity, and alphabet size). It has applications to computational complexity (in particular hardness of approximation) and cryptography. The definition of a probabilistically checkable proof was explicitly introduced by Arora and Safra in 1992, although their properties were studied earlier. In 1990 Babai, Fortnow, and Lund proved that PCP[poly(n), poly(n)] = NEXP, providing the first nontrivial equivalence between standard proofs (NEXP) and probabilistically checkable proofs.

The PCP theorem is the culmination of a long line of work on interactive proofs and probabilistically checkable proofs. The first theorem relating standard proofs and probabilistically checkable proofs is the statement that NEXP ⊆ PCP[poly(n), poly(n)], proved by .

The notation PCPc(n), s(n)[r(n), q(n)] is explained at Probabilistically checkable proof. The notation is that of a function that returns a certain complexity class. See the explanation mentioned above. The name of this theorem (the "PCP theorem") probably comes either from "PCP" meaning "probabilistically checkable proof", or from the notation mentioned above (or both).

In the past, checkable deposits were US banks’ most important source of funds; in 1960, checkable deposits comprised more than 60 percent of banks’ total liabilities. Over time, however, the composition of banks’ balance sheets has changed significantly. In lieu of customer deposits, banks have increasingly turned to short-term liabilities such as commercial paper (CP), certificates of deposit (CDs), repurchase agreements (repos), swapped foreign exchange liabilities, and brokered deposits.

Although it was shown that verifiable computing is possible in theory (using fully homomorphic encryption or via probabilistically checkable proofs), most of the known constructions are very expensive in practice. Recently, some researchers have looked at making verifiable computation practical. One such effort is the work of UT Austin researchers. The authors start with an argument system based on probabilistically checkable proofs and reduce its costs by a factor of 1020.

Alternatively, the unique games conjecture postulates the existence of a certain type of probabilistically checkable proof for problems in NP. A unique game can be viewed as a special kind of nonadaptive probabilistically checkable proof with query complexity 2, where for each pair of possible queries of the verifier and each possible answer to the first query, there is exactly one possible answer to the second query that makes the verifier accept, and vice versa. The unique games conjecture states that for every sufficiently small pair of constants ε, δ > 0 there is a constant K such that every problem in NP has a probabilistically checkable proof over an alphabet of size K with completeness 1 − δ, soundness ε and randomness complexity O(log(n)) which is a unique game.

However, this is not possible unless P = NP.This reduction is originally due to and used in all subsequent inapproximability proofs; the proofs differ in the strengths and details of the probabilistically checkable proof systems that they rely on.

The PCP theorem proved in 1992 states that PCP[O(log n),O(1)] = NP. The theory of hardness of approximation requires a detailed understanding of the role of completeness, soundness, alphabet size, and query complexity in probabilistically checkable proofs.

MFO Workshop Complexity Theory, Nov. 2009 Dana Moshkovitz Aaronson () is an Israeli theoretical computer scientist whose research topics include approximation algorithms and probabilistically checkable proofs. She is an associate professor of computer science at the University of Texas at Austin.

He was awarded the Gödel Prize twice, in 2001 and 2005, for his work on probabilistically checkable proofs and on the space complexity of approximating the frequency moments in streamed data.Gödel Prize website with list of winners He is married and has two daughters.

Probabilistically checkable proofs give rise to many complexity classes depending on the number of queries required and the amount of randomness used. The class PCP[r(n),q(n)] refers to the set of decision problems that have probabilistically checkable proofs that can be verified in polynomial time using at most r(n) random bits and by reading at most q(n) bits of the proof. Unless specified otherwise, correct proofs should always be accepted, and incorrect proofs should be rejected with probability greater than 1/2. The PCP theorem, a major result in computational complexity theory, states that PCP[O(log n),O(1)] = NP.

These are like Goldbach's conjecture, in stating that all natural numbers possess a certain property that is algorithmically checkable for each particular number.Thus, the Goldbach Conjecture itself can be expressed as saying that for each natural number n the number 2n+4 is the sum of two prime numbers.

Luca Trevisan (21 July 1971) is an Italian professor of computer science at Bocconi University in Milan. His research area is theoretical computer science, focusing on randomness, cryptography, probabilistically checkable proofs, approximation, property testing, spectral graph theory, and sublinear algorithms. He also runs a blog, in theory, about theoretical computer science.

In 2017 he was elected to the National Academy of Sciences.National Academy of Sciences Members and Foreign Associates Elected, National Academy of Sciences, 2 May 2017. Sudan has made important contributions to several areas of theoretical computer science, including probabilistically checkable proofs, non-approximability of optimization problems, list decoding, and error-correcting codes.

In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof. The algorithm is then required to accept correct proofs and reject incorrect proofs with very high probability. A standard proof (or certificate), as used in the verifier-based definition of the complexity class NP, also satisfies these requirements, since the checking procedure deterministically reads the whole proof, always accepts correct proofs and rejects incorrect proofs. However, what makes them interesting is the existence of probabilistically checkable proofs that can be checked by reading only a few bits of the proof using randomness in an essential way.

Irit Dinur (Hebrew: אירית דינור) is an Israeli mathematician. She is professor of computer science at the Weizmann Institute of Science.Faculty listing, Weizmann Institute Faculty of Mathematics and Computer Science, retrieved 2014-06-18. Her research is in foundations of computer science and in combinatorics, and especially in probabilistically checkable proofs and hardness of approximation.

Sanjeev Arora (born January 1968) is an Indian American theoretical computer scientist who is best known for his work on probabilistically checkable proofs and, in particular, the PCP theorem. He is currently the Charles C. Fitzmorris Professor of Computer Science at Princeton University, and his research interests include computational complexity theory, uses of randomness in computation, probabilistically checkable proofs, computing approximate solutions to NP-hard problems, geometric embeddings of metric spaces, and theoretical machine learning (especially deep learning). He received a B.S. in Mathematics with Computer Science from MIT in 1990 and received a Ph.D. in Computer Science from the University of California, Berkeley in 1994 under Umesh Vazirani. Earlier, in 1986, Sanjeev Arora had topped the IIT JEE but transferred to MIT after 2 years at IIT Kanpur.

M1 includes currency in circulation. It is the base measurement of the money supply and includes cash in the hands of the public, both bills and coins, plus peso demand deposits, tourists’ checks from non-bank issuers, and other checkable deposits. Basically, these are funds readily available for spending. Adjusted M1 is calculated by summing all the components mentioned above.

Ran Raz is well known for his work on interactive proof systems. His two most- cited papers are on multi-prover interactive proofs and on probabilistically checkable proofs.Citations counts for as of 21 Feb 2009: Google Scholar: 313, ISI Web of Knowledge: 120, ACM Digital Library: 57 + 17, MathSciNet: 53. Citations counts for as of 21 Feb 2009: Google Scholar: 314, ACM Digital Library: 71, MathSciNet: 59.

False negatives are not allowed: a valid proof must always be accepted. However, an invalid proof may sometimes mistakenly be accepted. For every invalid proof, the probability that the checker will accept it must be low. To transform a probabilistically checkable proof system of this type into a clique problem, one forms a graph with a vertex for each possible accepting run of the proof checker.

In the United States, transaction deposit is a term used by the Federal Reserve for checkable deposits and other accounts that can be used directly as cash without withdrawal limits or restrictions. Such deposits are subject to reserve requirements imposed by the central bank that require the bank to keep reserves at the central bank. This is in contrast to "time deposits" ( term deposits), which are not subject to reserve requirements.

In computer science, a property testing algorithm for a decision problem is an algorithm whose query complexity to its input is much smaller than the instance size of the problem. Typically property testing algorithms are used to decide if some mathematical object (such as a graph or a boolean function) has a "global" property, or is "far" from having this property, using only a small number of "local" queries to the object. For example, the following promise problem admits an algorithm whose query complexity is independent of the instance size (for an arbitrary constant ε > 0): :"Given a graph G on n vertices, decide if G is bipartite, or G cannot be made bipartite even after removing an arbitrary subset of at most \epsilon\tbinom n2 edges of G." Property testing algorithms are central to the definition of probabilistically checkable proofs, as a probabilistically checkable proof is essentially a proof that can be verified by a property testing algorithm.

Money is a means of final payment for goods in most price system economies, and is the unit of account in which prices are typically stated. Money has general acceptability, relative consistency in value, divisibility, durability, portability, elasticity in supply, and longevity with mass public confidence. It includes currency held by the nonbank public and checkable deposits. It has been described as a social convention, like language, useful to one largely because it is useful to others.

A rule is perhaps one of the simplest notions in computer science: it is an IF - THEN construct. If some condition (the IF part) that is checkable in some dataset holds, then the conclusion (the THEN part) is processed. Deriving somewhat from its roots in logic, rule systems use a notion of predicates that hold or not of some data object or objects. For example, the fact that two people are married might be represented with predicates as MARRIED(LISA,JOHN).

Locally testable codes have a lot in common with probabilistically checkable proofs (PCPs). This should be apparent from the similarities of their construction. In both, we are given q random nonadaptive queries into a large string and if we want to accept, we must with probability 1, and if not, we must accept no more than half the time. The major difference is that PCPs are interested in accepting x if there exists a w so that M^w(x)=1.

More specifically, for an ideal I in the ring k[x1, ..., xn] over a field k, a (Ritt) characteristic set C of I is composed of a set of polynomials in I, which is in triangular shape: polynomials in C have distinct main variables (see the formal definition below). Given a characteristic set C of I, one can decide if a polynomial f is zero modulo I. That is, the membership test is checkable for I, provided a characteristic set of I.

Sometimes it is only necessary to decode single bits of the message, or to check whether a given signal is a codeword, and do so without looking at the entire signal. This can make sense in a streaming setting, where codewords are too large to be classically decoded fast enough and where only a few bits of the message are of interest for now. Also such codes have become an important tool in computational complexity theory, e.g., for the design of probabilistically checkable proofs.

Many examples of problems with checkable algorithms come from graph theory. For instance, a classical algorithm for testing whether a graph is bipartite would simply output a Boolean value: true if the graph is bipartite, false otherwise. In contrast, a certifying algorithm might output a 2-coloring of the graph in the case that it is bipartite, or a cycle of odd length if it is not. Any graph is bipartite if and only if it can be 2-colored, and non- bipartite if and only if it contains an odd cycle.

The Bike Friday New World Tourist packs into an airline checkable suitcase that can be converted into a trailer and pulled behind the bicycle. The Raleigh Twenty, manufactured from 1968 to 1984, though still commonly available today second hand, is also a popular frame format used to construct collapsible touring bicycles. Other bicycles such as the Surly Travelers Check and the Santana Travel Tandem are full-sized bicycles which do not fold, but instead use Bicycle Torque Couplings to enable separating the frame into two parts for easier transport.

The condition of having no fixed prime divisor is certainly effectively checkable in a given case, since there is an explicit basis for the integer-valued polynomials. As a simple example, : x^2 + 1 has no fixed prime divisor. We therefore expect that there are infinitely many primes : n^2 + 1 This has not been proved, though. It was one of Landau's conjectures and goes back to Euler, who observed in a letter to Goldbach in 1752 that n^2 + 1 is often prime for n up to 1500.

By assuming a computationally bounded adversary, it is possibly to design a locally decodable code which is both efficient and near-optimal, with a negligible error probability. These codes are used in complexity theory for things like self-correcting computations, probabilistically checkable proof systems, and worst-case to average-case hardness reductions in the constructions of pseudo- random generators. They are useful in cryptography as a result of their connection with private information retrieval protocols. They are also in a number of database applications like fault-tolerant data storage.

In a probabilistically checkable proof system, a proof is represented as a sequence of bits. An instance of the satisfiability problem should have a valid proof if and only if it is satisfiable. The proof is checked by an algorithm that, after a polynomial- time computation on the input to the satisfiability problem, chooses to examine a small number of randomly chosen positions of the proof string. Depending on what values are found at that sample of bits, the checker will either accept or reject the proof, without looking at the rest of the bits.

So, Sudoku is in NP (quickly checkable) but does not seem to be in P (quickly solvable). Thousands of other problems seem similar, in that they are fast to check but slow to solve. Researchers have shown that many of the problems in NP have the extra property that a fast solution to any one of them could be used to build a quick solution to any other problem in NP, a property called NP-completeness. Decades of searching have not yielded a fast solution to any of these problems, so most scientists suspect that none of these problems can be solved quickly.

He was awarded the Rolf Nevanlinna Prize at the 24th International Congress of Mathematicians (ICM) in 2002. The prize recognizes outstanding work in the mathematical aspects of computer science. Sudan was honored for his work in advancing the theory of probabilistically checkable proofs--a way to recast a mathematical proof in computer language for additional checks on its validity--and developing error-correcting codes.. For the same work, he received the ACM's Distinguished Doctoral Dissertation Award in 1993 and the Gödel Prize in 2001 and was an Invited Speaker of the ICM in 1998. He is a Fellow of the ACM (2008).

While the journalistic view focuses on analysis, learning, information and objectivity. The cinematic uses creative cinematic devices, values the expression of opinion, foregrounds the point of view of the filmmaker and creative treatment is expected. On the other hand the journalistic, rational approach is founded upon checkable facts, has recourse to experts and eye witness testimony, the validity of filmmakers opinion is questioned and creative treatment rejected. De Bromhead wants to move away from problems of "objectivity and truth" and focus on issues of narrative and its "relationship to the represented". She understands that documentary’s "claim to the real" is subjective i.e.

A simpler, but related, problem is proof verification, where an existing proof for a theorem is certified valid. For this, it is generally required that each individual proof step can be verified by a primitive recursive function or program, and hence the problem is always decidable. Since the proofs generated by automated theorem provers are typically very large, the problem of proof compression is crucial and various techniques aiming at making the prover's output smaller, and consequently more easily understandable and checkable, have been developed. Proof assistants require a human user to give hints to the system.

In computational complexity theory, (SAT, ε-UNSAT) is a language that is used in the proof of the PCP theorem, which relates the language NP to probabilistically checkable proof systems. For a given 3-CNF formula, Φ, and a constant, ε < 1, Φ is in (SAT, ε-UNSAT) if it is satisfiable and not in (SAT, ε-UNSAT) if the maximum number of satisfiable clauses (MAX-3SAT) is less than or equal to (1-ε) times the number of clauses in Φ. If neither of these conditions are true, the membership of Φ in (SAT, ε-UNSAT) is undefined.

The Bankers is the 1975 book by the economist-writer Martin Mayer that describes the industry just at the cusp of deregulation. At the time, banks had just been released from the interest rate ceilings of Regulation Q imposed by the Fed. Also, NOW (or negotiable orders of withdrawal) accounts allowed checkable deposits to earn interest. This period, the mid to late 1970s saw an explosion of financial markets innovation with money market mutual fund accounts, call and put options traded first over the counter then on listed exchanges and finally bank deregulation as failed banks were taken over by out of state banks.

In the United States, a negotiable order of withdrawal account (NOW account) is a deposit account that pays interest on which an unlimited number of checks may be written. A negotiable order of withdrawal is essentially identical to a check drawn on a demand deposit account, but US banking regulations define the terms "demand deposit account" and "negotiable order of withdrawal account" separately. Until July 2011, Regulation Q stated that a demand deposit could not pay interest. NOW accounts were structured to comply with Regulation Q. NOW accounts are considered checkable deposits, and are counted in the Federal Reserve Board's M1 definition of the money supply, as well as in the broader definitions.

In theoretical computer science, a small-bias sample space (also known as \epsilon-biased sample space, \epsilon-biased generator, or small-bias probability space) is a probability distribution that fools parity functions. In other words, no parity function can distinguish between a small-bias sample space and the uniform distribution with high probability, and hence, small- bias sample spaces naturally give rise to pseudorandom generators for parity functions. The main useful property of small-bias sample spaces is that they need far fewer truly random bits than the uniform distribution to fool parities. Efficient constructions of small-bias sample spaces have found many applications in computer science, some of which are derandomization, error- correcting codes, and probabilistically checkable proofs.

His work in Complexity Theory includes the classification of approximation problems—showing them NP-hard even for weak factors of approximation—and the theory of probabilistically checkable proofs (PCP) and the PCP theorem, which gives stronger characterizations of the class NP, via a membership proof that can be verified reading only a constant number of its bits. His work on automata theory investigates determinization and complementation of finite automata over infinite strings, in particular, the complexity of such translation for Büchi automata, Streett automata and Rabin automata. In 2001, Safra won the Gödel Prize in theoretical computer science for his papers "Interactive Proofs and the Hardness of Approximating Cliques" and "Probabilistic Checking of Proofs: A New Characterization of NP".

In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically checkable. If the set of assumptions is empty, then the last sentence in a formal proof is called a theorem of the formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a proof of a given sentence or determine that none exists.

There are two main relaxations of QCQP: using semidefinite programming (SDP), and using the reformulation-linearization technique (RLT). For some classes of QCQP problems (precisely, QCQPs with zero diagonal elements in the data matrices), second- order cone programming (SOCP) and linear programming (LP) relaxations providing the same objective value as the SDP relaxation are available. Nonconvex QCQPs with non-positive off-diagonal elements can be exactly solved by the SDP or SOCP relaxations, and there are polynomial-time-checkable sufficient conditions for SDP relaxations of general QCQPs to be exact. Moreover, it was shown that a class of random general QCQPs has exact semidefinite relaxations with high probability as long as the number of constraints grows no faster than a fixed polynomial in the number of variables.

In terms of descriptive complexity theory, NP corresponds precisely to the set of languages definable by existential second-order logic (Fagin's theorem). NP can be seen as a very simple type of interactive proof system, where the prover comes up with the proof certificate and the verifier is a deterministic polynomial-time machine that checks it. It is complete because the right proof string will make it accept if there is one, and it is sound because the verifier cannot accept if there is no acceptable proof string. A major result of complexity theory is that NP can be characterized as the problems solvable by probabilistically checkable proofs where the verifier uses O(log n) random bits and examines only a constant number of bits of the proof string (the class PCP(log n, 1)).

Though the Federal Reserve authorizes and distributes the currency printed by the Treasury (the primary component of the narrow monetary base), the broad money supply is primarily created by commercial banks through the money multiplier mechanism. One textbook summarizes the process as follows: > "The Fed" controls the money supply in the United States by controlling the > amount of loans made by commercial banks. New loans are usually in the form > of increased checking account balances, and since checkable deposits are > part of the money supply, the money supply increases when new loans are made > ... This type of money is convertible into cash when depositors request cash withdrawals, which will require banks to limit or reduce their lending. The vast majority of the broad money supply throughout the world represents current outstanding loans of banks to various debtors.

In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity class has probabilistically checkable proofs (proofs that can be checked by a randomized algorithm) of constant query complexity and logarithmic randomness complexity (uses a logarithmic number of random bits). The PCP theorem says that for some universal constant K, for every n, any mathematical proof of length n can be rewritten as a different proof of length poly(n) that is formally verifiable with 99% accuracy by a randomized algorithm that inspects only K letters of that proof. The PCP theorem is the cornerstone of the theory of computational hardness of approximation, which investigates the inherent difficulty in designing efficient approximation algorithms for various optimization problems. It has been described by Ingo Wegener as "the most important result in complexity theory since Cook's theorem" and by Oded Goldreich as "a culmination of a sequence of impressive works […] rich in innovative ideas".

Lund was a co-author on two of five competing papers at the 1990 Symposium on Foundations of Computer Science characterizing complexity classes such as PSPACE and NEXPTIME in terms of interactive proof systems;.. Later published in JACM, 1991, .. Later published in Computational Complexity, 1991, . this work became part of his 1991 Ph.D. thesis from the University of Chicago under the supervision of Lance Fortnow and László Babai,. for which he was a runner- up for the 1991 ACM Doctoral Dissertation Award.. He is also known for his joint work with Sanjeev Arora, Madhu Sudan, Rajeev Motwani, and Mario Szegedy that discovered the existence of probabilistically checkable proofs for NP- hard problems and used them to prove hardness results for approximation problems;.. Originally presented at the 1992 Symposium on Foundations of Computer Science, . in 2001 he and his co-authors received the Gödel Prize for their share in these discoveries.. More recently he has published highly cited work on internet traffic engineering... He has been working for AT&T; Laboratories since August 1991.

A compatibility graph of partial words Two partial words are said to be compatible when they have the same length and when every position that is a non-wildcard in both of them has the same character in both. If one forms an undirected graph with a vertex for each partial word in a collection of partial words, and an edge for each compatible pair, then the cliques of this graph come from sets of partial words that all match at least one common string. This graph-theoretical interpretation of compatibility of partial words plays a key role in the proof of hardness of approximation of the clique problem, in which a collection of partial words representing successful runs of a probabilistically checkable proof verifier has a large clique if and only if there exists a valid proof of an underlying NP-complete problem. The faces (subcubes) of an n-dimensional hypercube can be described by partial words of length n over a binary alphabet, whose symbols are the Cartesian coordinates of the hypercube vertices (e.g.