We study multi-structural games, played on two sets $\mathcal{A}$ and $\mathcal{B}$ of structures. These games generalize Ehrenfeucht-Fra\"{i}ss\'{e} games. Whereas Ehrenfeucht-Fra\"{i}ss\'{e} games capture the quantifier rank of a first-order sentence, multi-structural games capture the number of quantifiers, in the sense that Spoiler wins the $r$-round game if and only if there is a first-order sentence $\phi$ with at most $r$ quantifiers, where every structure in $\mathcal{A}$ satisfies $\phi$ and no structure in $\mathcal{B}$ satisfies $\phi$. We use these games to give a complete characterization of the number of quantifiers required to distinguish linear orders of different sizes, and develop machinery for analyzing structures beyond linear orders.

The number of quantifiers needed to express first-order (FO) properties is captured by two-player combinatorial games called multi-structural games. We analyze these games on binary strings with an ordering relation, using a technique we call parallel play, which significantly reduces the number of quantifiers needed in many cases. Ordered structures such as strings have historically been notoriously difficult to analyze in the context of these and similar games. Nevertheless, in this paper, we provide essentially tight bounds on the number of quantifiers needed to characterize different-sized subsets of strings. The results immediately give bounds on the number of quantifiers necessary to define several different classes of Boolean functions. One of our results is analogous to Lupanov’s upper bounds on circuit size and formula size in propositional logic: we show that every Boolean function on n-bit inputs can be defined by a FO sentence having (1+ε)n/log(n) + O(1) quantifiers, and that this is essentially tight. We reduce this number to (1 + ε)log(n) + O(1) when the Boolean function in question is sparse.

Multi-structural (MS) games are combinatorial games that capture the number of quantifiers of first-order sentences. On the face of their definition, MS games differ from Ehrenfeucht-Fraisse (EF) games in two ways: first, MS games are played on two sets of structures, while EF games are played on a pair of structures; second, in MS games, Duplicator can make any number of copies of structures. In the first part of this paper, we perform a finer analysis of MS games and develop a closer comparison of MS games with EF games. In particular, we point out that the use of sets of structures is of the essence and that when MS games are played on pairs of structures, they capture Boolean combinations of first-order sentences with a fixed number of quantifiers. After this, we focus on another important difference between MS games and EF games, namely, the necessity for Spoiler to play on top of a previous move in order to win some MS games. Via an analysis of the types realized during MS games, we delineate the expressive power of the variant of MS games in which Spoiler never plays on top of a previous move. In the second part we focus on simultaneously capturing number of quantifiers and number of variables in first-order logic. We show that natural variants of the MS game do *not* achieve this. We then introduce a new game, the quantifier-variable tree game, and show that it simultaneously captures the number of quantifiers and number of variables. We conclude by generalizing this game to a family of games, the *syntactic games*, that simultaneously capture reasonable syntactic measures and the number of variables.

In 1981, Neil Immerman described a two-player game, which he called the "separability game" \cite{Immerman81}, that captures the number of quantifiers needed to describe a property in first-order logic. Immerman's paper laid the groundwork for studying the number of quantifiers needed to express properties in first-order logic, but the game seemed to be too complicated to study, and the arguments of the paper almost exclusively used quantifier rank as a lower bound on the total number of quantifiers. However, last year Fagin, Lenchner, Regan and Vyas rediscovered the games, provided some tools for analyzing them, and showed how to utilize them to characterize the number of quantifiers needed to express linear orders of different sizes. In this paper, we push forward in the study of number of quantifiers as a bona fide complexity measure by establishing several new results. First we carefully distinguish minimum number of quantifiers from the more usual descriptive complexity measures, minimum quantifier rank and minimum number of variables. Then, for each positive integer $k$, we give an explicit example of a property of finite structures (in particular, of finite graphs) that can be expressed with a sentence of quantifier rank $k$, but where the same property needs $2^{Ω(k^2)}$ quantifiers to be expressed.

This paper proposes a research direction to advance AI which draws inspiration from cognitive theories of human decision making. The premise is that if we gain insights about the causes of some human capabilities that are still lacking in AI (for instance, adaptability, generalizability, common sense, and causal reasoning), we may obtain similar capabilities in an AI system by embedding these causal components. We hope that the high-level description of our vision included in this paper, as well as the several research questions that we propose to consider, can stimulate the AI research community to define, try and evaluate new methodologies, frameworks, and evaluation metrics, in the spirit of achieving a better understanding of both human and machine intelligence.

We study multi-structural games, played on two sets ${\mathcal{A}}$ and ${\mathcal{B}}$ of structures. These games generalize Ehrenfeucht-Fraïssé games. Whereas Ehrenfeucht-Fraïssé games capture the quantifier rank of a first-order sentence, multi-structural games capture the number of quantifiers, in the sense that Spoiler wins the r-round game if and only if there is a first-order sentence ϕ with at most r quantifiers, where every structure in ${\mathcal{A}}$ satisfies ϕ and no structure in ${\mathcal{B}}$ satisfies ϕ. We use these games to give a complete characterization of the number of quantifiers required to distinguish linear orders of different sizes, and develop machinery for analyzing structures beyond linear orders.

Farmers in rural areas of Kenya generally rely on traditional agricultural practices inherited from past generations. However, population increases and climate changes have put pressure on resources such as land and water. These resource pressures have created a need to broaden and expand farming practices. We conducted an exploratory study with farmers in Tharaka Nithi, Kenya to explore their practices, if and how they used ICT, and how the technologies used might be designed to aid their practices, if at all. Overall, our results show that farmers desired more knowledge to enable them apply ICT interventions in ways that improved yields. Farmers were also interested in accessing information on soil fertility, water predictability and market opportunities. These findings suggest opportunities for technology design to support farming practices among rural communities in rural settings. We also articulate social challenges that designers will face when thinking about coming up with such solutions.

We describe the effective use of online learning to enhance the conversational capabilities of a concierge robot that we have been developing over the last two years. The robot was designed to interact naturally with visitors and uses a speech recognition system in conjunction with a natural language classifier. The online learning component monitors interactions and collects explicit and implicit user feedback from a conversation and feeds it back to the classifier in the form of new class instances and adjusted threshold values for triggering the classes. In addition, it enables a trusted master to teach it new question-answer pairs via question-answer paraphrasing, and solicits help with maintaining question-answer-class relationships when needed, obviating the need for explicit programming. The system has been completely implemented and demonstrated using the SoftBank Robotics humanoid robots Pepper and NAO, and the telepresence robot known as Double from Double Robotics.

Management and monitoring of data centers is a growing field of interest, with much current research, and the emergence of a variety of commercial products aiming to improve performance, resource utilization and energy efficiency of the computing infrastructure. Despite the large body of work on optimizing data center operations, few studies actually focus on discovering and tracking the physical layout of assets in these centers. Such asset tracking is a prerequisite to faithfully performing administration and any form of optimization that relies on physical layout characteristics.

Major advances in Question Answering technology were needed for IBM Watson to play Jeopardy! at championship level -- the show requires rapid-fire answers to challenging natural language questions, broad general knowledge, high precision, and accurate confidence estimates. In addition, Jeopardy! features four types of decision making carrying great strategic importance: (1) Daily Double wagering; (2) Final Jeopardy wagering; (3) selecting the next square when in control of the board; (4) deciding whether to attempt to answer, i.e., "buzz in." Using sophisticated strategies for these decisions, that properly account for the game state and future event probabilities, can significantly boost a player's overall chances to win, when compared with simple "rule of thumb" strategies. This article presents our approach to developing Watson's game-playing strategies, comprising development of a faithful simulation model, and then using learning and Monte-Carlo methods within the simulator to optimize Watson's strategic decision-making. After giving a detailed description of each of our game-strategy algorithms, we then focus in particular on validating the accuracy of the simulator's predictions, and documenting performance improvements using our methods. Quantitative performance benefits are shown with respect to both simple heuristic strategies, and actual human contestant performance in historical episodes. We further extend our analysis of human play to derive a number of valuable and counterintuitive examples illustrating how human contestants may improve their performance on the show.

We describe an inexpensive autonomous robot capable of navigating previously unseen data centers and monitoring key metrics such as air temperature. The robot provides real-time navigation and sensor data to commercial IBM software, thereby enabling real-time generation of the data center layout, a thermal map and other visualizations of energy dynamics. Once it has mapped a data center, the robot can efficiently monitor it for hot spots and other anomalies using intelligent sampling. We demonstrate the robot's effectiveness via experimental studies from two production data centers.

We will demonstrate a robot for data center energy management, in action, on a simulated data center floor. We shall highlight the robot's navigation, tile and obstacle classification, event scheduling and preemption capabilities, along with its ability to discover charging docks, and successfully dock with extreme precision. We shall also show simulations on real data center layouts evincing navigational efficiency gains obtained by our latest heuristic enhancements.

We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (tj) and radii (rj) that cover a given set of demand points Y∈R2 at the smallest possible cost. We consider cost functions of the form Εjf(rj), where f(r)=rα is the cost of transmission to radius r. Special cases arise for α=1 (sum of radii) and α=2 (total area); power consumption models in wireless network design often use an exponent α>2. Different scenarios arise according to possible restrictions on the transmission centers tj, which may be constrained to belong to a given discrete set or to lie on a line, etc.We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points tj on a given line in order to cover demand points Y∈R2; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y; (c) a proof of NP-hardness for a discrete set of transmission points in R2 and any fixed α>1; and (d) a polynomial-time approximation scheme for the problem of computing a minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of disks and the length of a tour/path that connects the centers of the disks.