Related papers: Threefold Post Correspondence System
We define the symmetric Post Correspondence Problem (PCP) and prove that it is undecidable. As an application we show that the original proof of undecidability of the freeness problem for 3-by-3 integer matrix semigroups works for the…
In 1946 Emil Leon Post (Bulletin of Amer. Math. Soc. 52 (1946), 264 - 268) defined a famous correspondence decision problem which is nowadays called the Post Correspondence Problem, and he proved that the problem is undecidable. In this…
We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…
We suggest a method of solving the problem of existence of a triangle with prescribed two bisectors and one third element which can be taken as one of the angles, the sides, the heights or the medians, or the third bisector.
Let PCP(k) denote the Post Correspondence Problem for k input pairs of strings. Let ACCESSIBILITY(k) denote the the word problem for k-rule semi-Thue systems. In 1980, Claus showed that if ACCESSIBILITY(k) is undecidable then PCP(k + 4) is…
Determining dense semantic correspondences across objects and scenes is a difficult problem that underpins many higher-level computer vision algorithms. Unlike canonical dense correspondence problems which consider images that are spatially…
The Post Correspondence Problem is a classical decision problem about equalisers of free monoid homomorphisms. We prove connections between several variations of this classical problem, but in the setting of free groups and free group…
We seek a practical method for establishing dense correspondences between two images with similar content, but possibly different 3D scenes. One of the challenges in designing such a system is the local scale differences of objects…
Conversational recommender systems have demonstrated great success. They can accurately capture a user's current detailed preference -- through a multi-round interaction cycle -- to effectively guide users to a more personalized…
Cyber physical systems CPSs embodies the conception as well as the implementation of the integration of the state-of-art technologies in sensing, communication, computing, and control. Such systems incorporate new trends such as cloud…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
Computer vision has long relied on two kinds of correspondences: pixel correspondences in images and 3D correspondences on object surfaces. Is there another kind, and if there is, what can they do for us? In this paper, we introduce…
This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability. This argument is based on an…
Communicating finite-state machines (CFMs) are a Turing powerful model of asynchronous message-passing distributed systems. In weakly synchronous systems, processes communicate through phases in which messages are first sent and then…
This paper addresses the problem of handling spatial misalignments due to camera-view changes or human-pose variations in person re-identification. We first introduce a boosting-based approach to learn a correspondence structure which…
We present a simple yet effective method for 3D correspondence grouping. The objective is to accurately classify initial correspondences obtained by matching local geometric descriptors into inliers and outliers. Although the spatial…
This paper presents a thorough evaluation of several widely-used 3D correspondence grouping algorithms, motived by their significance in vision tasks relying on correct feature correspondences. A good correspondence grouping algorithm is…
Computer systems have evolved over the years starting from sizable, single-user, slow, and expensive machines to multi-user, fast, cheaper, and small-sized machines. The use of multi-user computer networks has given rise to a new paradigm…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
We propose and study a new class of gradient communication mechanisms for communication-efficient training -- three point compressors (3PC) -- as well as efficient distributed nonconvex optimization algorithms that can take advantage of…