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About 7,740 papers for “Counterexample”

Counterexample

Cr Submanifold An Addendum, Sun Luk, Stephen S. -t. Yau · 1998

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Counterexample

Fedor Nazarov Serguei Treil, Alexander Volberg · 2014

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Counterexample Machine

Christopher Hoffman · 1999

. We present a general method for constructing families of measure preserving transformations which are K and loosely Bernoulli with various ergodic theoretical properties. For example, we construct two K transformations which are weakly isomorphic but not isomorphic, and a K transformation with no roots. Ornstein's isomorphism theorem says families of Bernoulli shifts cannot have these properties [6]. The construction uses a combination of properties from maps constructed by Ornstein and Shields, and Rudolph, and reduces the question of isomorphism of two transformations to the conjugacy of two related permutations [10][13]. 1. Introduction By showing that any two Bernoulli shifts of the same entropy are isomorphic, Ornstein proved that there are a large number of ergodic theoretical properties that a collection of Bernoulli shifts cannot have. Many families of transformations have been constructed to show the contrast between Bernoulli shifts and K transformations. For examp...

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A counterexample

Best, E. · Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft) · 1983

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A counterexample

Best, E. · Fraunhofer-Publica (Fraunhofer-Gesellschaft) · 1983

S.8-9

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Frankfurt counterexample defended

Nucci Ezio Di · PhilPapers (PhilPapers Foundation) · 2011

Frankfurt sets out to refute the principle according to which ‘a person is morally responsible for what he has done only if he could have done otherwise’ . Frankfurt devises a counterexample in which an agent is intuitively responsible even though she could not have done otherwise: Suppose someone – Black, let us say – wants Jones to perform a certain action. Black is prepared to go to considerable lengths to get his way, but he prefers to avoid showing his hand unnecessarily. So he waits until Jones is about to make up his mind what to do, and he does nothing unless it is clear to him that Jones is going to decide to do something other than what he wants him to do. If it does become clear that Jones is going to decide to do something else, Black takes effective steps to ensure that Jones decides to do, and that he does do, what he wants him to do. Whatever Jones's initial preferences and inclinations, then, Black will have his way … Now suppose that Black never has to show his hand because Jones, for reasons of his own, decides to perform and does perform the very action Black wants him to perform. In that case, it seems clear, Jones will bear precisely …

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Jarzynski Equality Counterexample?

Ronald F. Fox · arXiv (Cornell University) · 2021

Almost 25 years ago, Jarzynski published a paper in which it was asserted: the work done, W, in driving a system from state A to state B, characterized by the Helmholtz free energies FA and FB, satisfies an equality in which an average over an ensemble of measurements for W determines the difference in Free energy. Several features of this result require more detailed description, to be given in the text. The equality is significant and unexpected. So is the statement that the equality is independent of the rate of change from state A to state B. A few years ago, I had presented three papers in which the contraction of the description from full phase space to coordinate space only was made. This was motivated by the large difference in time scales for momenta relaxation and coordinate relaxation. The Jarzynski equality (JE) will be shown here to be correct only in the limit of extremely slow processes. The proposed counterexample is for a macromolecular harmonic oscillator with a Hooke's spring constant, k, that during the time interval linearly changes from k1 to k2. When performed very slowly, we obtain JE in a form in which the free energy is related to the ratio of the k's. However, when the transition is performed more rapidly the equality is lost. Jarzynski has suggested to me that Hummer and Szabo have shown that JE follows directly from the Feynman-Kac formula. We show here that F-K does not reproduce the direct calculation executed in this paper and that it has been misapplied in earlier papers.

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The Counterexample Fallacy

2008

Abstract. Manley and Wasserman (2008) joins the chorus of opposition to the possibility of conditional analysis of dispositions. But that score cannot be settled without more careful attention to the implicit philosophical methodology. Some of the opposition to such an analysis badly overestimates the effect of counterexamples, as if the Gettier example were sufficient to refute the possibility of conjunctive analysis of knowledge. A general objection to a form of analysis must satisfy a number of constraints, and Manley and Wasserman joins the chorus too in failing to satisfy them. Most significant is the optional presupposition that the conditional used in analysis will exhibit some sort of centering. We show that even a careful effort to repair and reform Manley and Wassermans objection into a satisfactory argument requires, ultimately, appeal to centering. Worse, the particular positive proposal they offer is subject to a minor variant of their own counterexample. 1. How To Do Things With Counterexamples The ‘conditional fallacy ’ literature has endowed us with a delightful bestiary of counterexamples: electrofinks1, shy but intuitive chameleons2, divine agents (and sorcerers and angels) protecting crystal glasses3, glasses packed in styrofoam4, poisons and antidotes5, kazoos with wax-

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Counterexample-Guided Commutativity

Marcel Ebbinghaus, Dominik Klumpp, Andreas Podelski · Lecture notes in computer science · 2025

Abstract We consider the use of commutativity-based reduction for the algorithmic verification of concurrent programs. In existing work, the commutativity relation used for the reduction is mostly fixed statically. In this paper, we propose a demand-driven approach to compute the commutativity relation. The approach can be viewed as the direct analogue of the CEGAR approach which uses counterexamples to guide the incremental refinement of the abstraction. Instead of eliminating a counterexample by proving it infeasible and refining the abstraction, we can eliminate a counterexample by proving it redundant and expanding the commutativity relation. When we prove a counterexample redundant, we use the proof for a generalization step which allows us to eliminate not just a single counterexample, but a whole infinite set. We present a general scheme where we integrate the new approach with the CEGAR approach. We have implemented an instantiation of the general scheme. An experimental evaluation shows an increase in the number of successfully verified programs by 15% on a challenging benchmark set.

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Counterexample-guided Planning

Krishnendu Chatterjee, Thomas A. Henzinger, Ranjit Jhala et al. · arXiv (Cornell University) · 2012

Planning in adversarial and uncertain environments can be modeled as the problem of devising strategies in stochastic perfect information games. These games are generalizations of Markov decision processes (MDPs): there are two (adversarial) players, and a source of randomness. The main practical obstacle to computing winning strategies in such games is the size of the state space. In practice therefore, one typically works with abstractions of the model. The diffculty is to come up with an abstraction that is neither too coarse to remove all winning strategies (plans), nor too fine to be intractable. In verification, the paradigm of counterexample-guided abstraction refinement has been successful to construct useful but parsimonious abstractions automatically. We extend this paradigm to probabilistic models (namely, perfect information games and, as a special case, MDPs). This allows us to apply the counterexample-guided abstraction paradigm to the AI planning problem. As special cases, we get planning algorithms for MDPs and deterministic systems that automatically construct system abstractions.

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Confirmation Not Counterexample

Justin A. Capes · 2023

Abstract This concluding chapter provides a summary of the previous four chapters and explains how the fine-grained analysis defended in those chapters ultimately vindicates the principle of alternative possibilities (PAP). It is argued that we have reason to be suspicious of, and ultimately to reject, our initial intuition that agents in Frankfurt cases are morally responsible for doing what they couldn’t have avoided doing and, consequently, that Frankfurt cases aren’t counterexamples to the principle. It is further argued that, given the fine-grained analysis of the Frankfurt cases defended in the preceding chapters, the Frankfurt cases actually provide further confirmation of PAP.

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DSBS-MutInf-counterexample

Pichler, Georg · Figshare · 2017

Complementary material for "Distributed Information-Theoretic Clustering" We provide counterexamples to Conjecture 1 in<br> M. B. Westover and J. A. O’Sullivan, “Achievable rates for pattern recognition,” <br> IEEE Trans. Inf. Theory, vol. 54, no. 1, pp. 299–320, Jan. 2008. This code is written in the Octave programming language.

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Counterexample for Beal's Conjecture

Vega, Frank · Figshare · 2018

The Beal's conjecture states if $A^{x} + B^{y} = C^{z}$, where $A$, $B$, $C$, $x$, $y$ and $z$ are positive integers, $x$, $y$ and $z$ are all greater than $2$, then $A$, $B$ and $C$ must have a common prime factor. We show a counterexample for this conjecture.

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Ramsification and Glymour's Counterexample

David Braddon‐Mitchell, Robert Nola · Analysis · 1997

Journal Article Ramsification and Glymour’s Counterexample Get access David Braddon-Mitchell, David Braddon-Mitchell University of AucklandPrivate Bag 92019, Auckland, New Zealanddbm@auckland.ac.nzr.nola@auckland.ac.nz Search for other works by this author on: Oxford Academic Google Scholar Robert Nola Robert Nola University of AucklandPrivate Bag 92019, Auckland, New Zealanddbm@auckland.ac.nzr.nola@auckland.ac.nz Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 57, Issue 3, July 1997, Pages 167–169, https://doi.org/10.1093/analys/57.3.167 Published: 01 July 1997

Cited by 1

Kesten's Yaglom limit counterexample

Termeh Kousha · uO Research (University of Ottawa) · 2007

We consider a positive matrix Q, with entries {1,2,...}. Kesten showed that if there exists a constant 1 ≤ L &lt; infinity and sequences u1 &lt; u 2 &lt; ... and d1 &lt; d 2 &lt; ... such that Q(i, j) = 0 whenever i &lt; ur &lt; ur + L &lt; j or i &gt; dr + L &gt; dr &gt; j for some r, then if Q is also substochastic, it has the strong ratio limit property, that is, limn→infinity Qn+mi,j Qnk,l =R-mfim jfk ml for a suitable R and some R-1-harmonic function f and R-1-invariant measure mu. In this thesis, we delve into a counterexample of Kesten that shows that for a positive irreducible matrix Q, that is the transition probability matrix of a Markov chain {Xn}, the Yaglom limit theorem is not valid if we drop one of the restriction imposed above, even when Q has a minimal normalized quasi-stationary distribution. In the last section, we show the ratio limit property must also then fail.

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