Rank Logic is Dead, Long Live Rank Logic!

Motivated by the search for a logic for polynomial time, we study rank logic (FPR) which extends fixed-point logic with counting (FPC) by operators that determine the rank of matrices over finite fields. While FPR can express most of the known queries that separate FPC from PTIME, nearly nothing was known about the limitations of its expressive power. In our first main result we show that the extensions of FPC by rank operators over different prime fields are incomparable. This solves an open question posed by Dawar and Holm and also implies that rank logic, in its original definition with a distinct rank operator for every field, fails to capture polynomial time. In particular we show that the variant of rank logic FPR* with an operator that uniformly expresses the matrix rank over finite fields is more expressive than FPR. One important step in our proof is to consider solvability logic FPS which is the analogous extension of FPC by quantifiers which express the solvability problem for linear equation systems over finite fields. Solvability logic can easily be embedded into rank logic, but it is open whether it is a strict fragment. In our second main result we give a partial answer to this question: in the absence of counting, rank operators are strictly more expressive than solvability quantifiers

Towards Assume-Guarantee Profiles for Autonomous Vehicles

Rules or specifications for autonomous vehicles are currently formulated on a case-by-case basis, and put together in a rather ad-hoc fashion. As a step towards eliminating this practice, we propose a systematic procedure for generating a set of supervisory specifications for self-driving cars that are 1) associated with a distributed assume-guarantee structure and 2) characterizable by the notion of consistency and completeness. Besides helping autonomous vehicles make better decisions on the road, the assume-guarantee contract structure also helps address the notion of blame when undesirable events occur. We give several game-theoretic examples to demonstrate applicability of our framework

Peirce's sign theory as an open-source R package.

Throughout Peirce’s writing, we witness his developing vision of a machine that scientists will eventually be able to create. Nadin (2010) raised the question:Why do computer scientists continue to ignore Peirce’s sign theory? A review of the literature on Peirce’s theory and the semiotics machine reveals that many authors discussed the machine;however, they donot differentiate between a physical computer machine and its software. This paper discusses the problematic issues involved in converting Peirce’s theory into a programming language, machine and software application. We demonstrate this challenge by introducing Peirce’s sign theory as a software application that runs under an open-source R environmen

Data Structures and Algorithms for Disjoint Set Union Problems

This paper surveys algorithmic techniques and data structures that have been proposed to solve the set union problem and its variants. Their discovery required a new set of algorithmic tools that have proven useful in other areas. Special attention is devoted to recent extensions of the original set union problem, and some effort is made to provide a unifying theoretical framework for this growing body of algorithms

Partial Product Updates for Agents of Detectable Failure and Logical Obstruction to Task Solvability

The logical method proposed by Goubault, Ledent, and Rajsbaum provides a novel way to show the unsolvability of distributed tasks by means of a logical obstruction, which is an epistemic logic formula describing the reason of unsolvability. In this paper, we introduce the notion of partial product update, which refines that of product update in the original logical method, to encompass distributed tasks and protocols modeled by impure simplicial complexes. With this extended notion of partial product update, the original logical method is generalized so that it allows the application of logical obstruction to show unsolvability results in a distributed environment where the failure of agents is detectable. We demonstrate the use of the logical method by giving a concrete logical obstruction and showing that the consensus task is unsolvable by the single-round synchronous message-passing protocol

An American prototopia: or Peachtree City as an inadvertent, sustainable solution to urban sprawl

Peachtree City is a city with a secondary transportation network, known as the path system. This paperseeks to determine why the path system is so successful and whether there are fundamental spatial,configurational properties which underpin its achievement. This paper examines the axial-line network ofpaths as a distinct network then as part of the larger, combined system of both paths and roads.The finding of this paper is that the cart path system, although unintelligible in its own right, serves thepurpose of reducing the overall number of cul-de-sacs in the city whilst increasing its axial ringiness. Anew measure for calculating the spatial signature of sprawl is suggested - the proportion and distribution ofcircuit lengths in the axial map. The paper continues by discussing the social, economic and environmentalbenefits of the path system, with the proviso that these benefits arise only from a successful system and thata partial factor contributing to this must be the spatial regularities revealed in the axial analyses. It concludsby suggesting that without the cart path system, Peachtree City would consist of nothing more thanaggregations of typical suburban developments with one or two primary road-entrances accessed fromarterial-roads and containing a high ratio of cul-de-sacs.This paper concludes by suggesting how Peachtree City could be held to be the blue-print of a ?protopia?,presenting a principle by which American suburbia could be transformed into sustainable communities andyet do so in a manner which would be distinctly American in character and hence palatable to its residentsunlike many current, public-transport focused proposals

How can start-ups increase their value co-creation through SEO?

Abstract. The internet started in the 1960s for government researchers to exchange research. Tim Berners Lee created the foundation for the web in 1990, which consisted of the HTTP protocol, a browser, a server, and the world’s first website. Netscape, an early web browser, had a very successful IPO in 1995, which ultimately popularized the web and sparked the so-called “Dot Com bubble.” The World Wide Web, since its creation until now, has become a critical channel between companies and customers. Over half of the internet starts their search on a search engine, making it imperative for companies that want to stay competitive to have a website online. Ever since the commercialization of the internet, startup companies have competed for the first search results in search engines through a digital marketing technique known as Search Engine Optimization. SEO as a study topic has been studied since Google was created in 1998. This thesis explores how value co-creation is created with Search Engine Optimization and how the two concepts are related. The context is for high-growth start-up companies that aim to increase their digital presence online. The research method is qualitative dominant and takes an abductive approach. The primary data was collected from a young startup company in North America and consisted of an extensive data set of user behavior. The data consisted of screen recordings of the users and user metrics collected through a tracking script on the website. The secondary data used takes the form of peer-reviewed articles, previous SEO studies, online articles, and books. Search Engine Optimization was found to enable companies that want to increase their value co-creation based on the data. It was shown to have the capacity to boost their online presence, create more opportunities for value co-creation, and provide an insight into any blockages preventing co-creation. Essentially, SEO was found to be a vehicle to drive users to companies’ websites and increase the chances for the company to engage the user with a value proposition that could later turn into value-creation. The data also revealed that companies could choose to become co-creators in value if they choose to do so. This was a contrary finding to the pre-existing theory

Salvaging Pascal’s Wager

Many think that Pascal’s Wager is a hopeless failure. A primary reason for this is because a number of challenging objections have been raised to the wager, including the “many gods” objection and the “mixed strategy” objection. We argue that both objections are formal, but not substantive, problems for the wager, and that they both fail for the same reason. We then respond to additional objections to the wager. We show how a version of Pascalian reasoning succeeds, giving us a reason to pay special attention to the infinite consequences of our actions