Single-agent search is a powerful tool for solving a variety of applications. Most of the application domains used to explore single-agent search techniques have the property that if you start with a solvable state, at no time in the search can you reach a state that is unsolvable. In this paper we address the implications that arise when state transitions can lead to unsolvable (deadlock) stat...

We prove NP-hardness of a wide class of pushing-block puzzles similar to the classic Sokoban, generalizing several previous results [5, 6, 9, 10, 15, 17]. The puzzles consist of unit square blocks on an integer lattice; all blocks are movable. The robot may move horizontally and vertically in order to reach a specified goal position. The puzzle variants differ in the number of blocks that the r...

Existing machine-learning work has shown that algorithms can benefit from curricula—learning first on simple examples before moving to more difficult examples. While most existing work on curriculum learning focuses on developing automatic methods to iteratively select training examples with increasing difficulty tailored to the current ability of the learner, relatively little attention has be...

Digraphs in which ordered pairs of outand in-degrees of vertices are mutually distinct are called irregular, see Gargano et al. [3]. Our investigations focus on the problem: what are possible sizes of irregular digraphs (oriented graphs) for a given order n? We show that those sizes in both cases make up integer intervals. The extremal sizes (the 612 Z. Dziechcińska-Halamoda, Z. Majcher, ... en...

Artificial intelligence (AI) research has developed an extensive collection of methods to solve state-space problems. Using the challenging domain of Sokoban, this paper studies the effect of general search enhancements on program performance. We show that the current state of the art in AI generally requires a large research and programming effort to use domain-dependent knowledge to solve eve...

The game “Reflections” is a puzzle game that has been around and entertaining users in various versions for many years. A single player tries to hit a given set of light bulbs with a laser beam, by placing mirrors and other optical items on grid cells. In this document, we investigate the complexity of the game, and show that deciding whether a given level has a solution is NP-complete. This is...

Despite major progress in AI planning over the last few years, many interesting domains remain challenging for current planners. Topological abstraction can reduce planning complexity in several domains, decomposing a problem into a two-level hierarchy. This paper presents LAP, a planning model based on topological abstraction. In formalizing LAP as a generic planning framework, the support of ...

We prove PSPACE-completeness of a class of pushingblock puzzles similar to the classic Sokoban, extending several previous results [1, 5, 12]. The puzzles consist of unit square blocks on an integer lattice; some of the blocks are movable. The robot may move horizontally and vertically in order to reach a specified goal position. The puzzle variants differ in the number of blocks that the robot...