The Alcuin number of a graph and its connections to the vertex cover number

We consider a planning problem that generalizes Alcuin's river crossing problem to scenarios with arbitrary conflict graphs. This generalization leads to the so-called Alcuin number of the underlying conflict graph. We derive a variety of combinatorial, structural, algorithmical, and complexity theoretical results around the Alcuin number. Our technical main result is an NP-certificate for the Alcuin number. It turns out that the Alcuin number of a graph is closely related to the size of a minimum vertex cover in the graph, and we unravel several surprising connections between these two graph parameters. We provide hardness results and a fixed parameter tractability result for computing the Alcuin number. Furthermore we demonstrate that the Alcuin number of chordal graphs, bipartite graphs, and planar graphs is substantially easier to analyze than the Alcuin number of general graphs

Knowledge Selection in Category-Based Inductive Reasoning

Current theories of category-based inductive reasoning can be distinguished by the emphasis they place on structured and unstructured knowledge. Theories which draw on unstructured knowledge focus on associative strength, or temporal and spatial contiguity between categories. In contrast, accounts which draw on structured knowledge make reference to the underlying theoretical frameworks which relate categories to one another, such as causal or taxonomic relationships. In this thesis, it is argued that this apparent dichotomy can be resolved if one ascribes different processing characteristics to these two types of knowledge. That is, unstructured knowledge influences inductive reasoning effortlessly and relatively automatically, whereas the use of structured knowledge requires effort and the availability of cognitive resources. Understanding these diverging processes illuminates how background knowledge is selected during the inference process. The thesis demonstrates that structured and unstructured knowledge are dissociable and influence reasoning in line with their unique processing characteristics. Using secondary task and speeded response paradigms, it shows that unstructured knowledge is most influential when people are cognitively burdened or forced to respond fast, whereas they can draw on more elaborate structured knowledge if they are not cognitively compromised. This is especially evident for the causal asymmetry effect, in which people make stronger inferences from cause to effect categories, than vice versa. This Bayesian normative effect disappears when people have to contend with a secondary task or respond under time pressure. The next experiments demonstrate that this dissociation between structured and unstructured knowledge is also evident for a more naturalistic inductive reasoning paradigm in which people generate their own inferences. In the final experiments, it is shown how the selection of appropriate knowledge ties in with more domain-general processes, and especially inhibitory control. When responses based on structured and unstructured knowledge conflict, people’s ability to reason based on appropriate structured knowledge depends upon having relevant background knowledge and on their ability to inhibit the lure from inappropriate unstructured knowledge. The thesis concludes with a discussion of how the concepts of structured and unstructured knowledge illuminate the processes underlying knowledge selection for category-based inductive reasoning. It also looks at the implications the findings have for different theories of category-based induction, and for our understanding of human reasoning processes more generally

The Computational Complexity of Some Games and Puzzles With Theoretical Applications

The subject of this thesis is the algorithmic properties of one- and two-player games people enjoy playing, such as Sudoku or Chess. Questions asked about puzzles and games in this context are of the following type: can we design efficient computer programs that play optimally given any opponent (for a two-player game), or solve any instance of the puzzle in question? We examine four games and puzzles and show algorithmic as well as intractability results. First, we study the wolf-goat-cabbage puzzle, where a man wants to transport a wolf, a goat, and a cabbage across a river by using a boat that can carry only one item at a time, making sure that no incompatible items are left alone together. We study generalizations of this puzzle, showing a close connection with the Vertex Cover problem that implies NP-hardness as well as inapproximability results. Second, we study the SET game, a card game where the objective is to form sets of cards that match in a certain sense using cards from a special deck. We study single- and multi-round variations of this game and establish interesting con- nections with other classical computational problems, such as Perfect Multi- Dimensional Matching, Set Packing, Independent Edge Dominating Set, and Arc Kayles. We prove algorithmic and hardness results in the classical and the parameterized sense. Third, we study the UNO game, a game of colored numbered cards where players take turns discarding cards that match either in color or in number. We extend results by Demaine et. al. (2010 and 2014) that connected one- and two-player generaliza- tions of the game to Edge Hamiltonian Path and Generalized Geography, proving that a solitaire version parameterized by the number of colors is fixed param- eter tractable and that a k-player generalization for k greater or equal to 3 is PSPACE-hard. Finally, we study the Scrabble game, a word game where players are trying to form words in a crossword fashion by placing letter tiles on a grid board. We prove that a generalized version of Scrabble is PSPACE-hard, answering a question posed by Demaine and Hearn in 2008

A workbook to accompany All Around Us, science book for grade two

Thesis (Ed.M.)--Boston Universit

Matita Tutorial

This tutorial provides a pragmatic introduction to the main functionalities of the Matita interactive theorem prover, offering a guided tour through a set of not so trivial examples in the field of software specification and verification.\u

The effect of the integration of science teaching by television on the development of scientific reasoning in the fifth grade student

Thesis (Ed.D.)--Boston University