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In scientific disciplines, a toy problem [1] [2] or a puzzlelike problem [3] is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique. A toy problem is useful to test and demonstrate methodologies. Researchers can use toy problems to compare the performance of different algorithms. They are also good for game designing.
For instance, while engineering a large system, the large problem is often broken down into many smaller toy problems which have been well understood in detail. Often these problems distill a few important aspects of complicated problems so that they can be studied in isolation. Toy problems are thus often very useful in providing intuition about specific phenomena in more complicated problems.
As an example, in the field of artificial intelligence, classical puzzles, games and problems are often used as toy problems. These include sliding-block puzzles, N-Queens problem, missionaries and cannibals problem, tic-tac-toe, chess, [1] Tower of Hanoi and others. [2] [3]
Artificial intelligence (AI) is the intelligence of machines or software, as opposed to the intelligence of humans or other living beings. It is a field of study in computer science that develops and studies intelligent machines. Such machines may be called AIs.
In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems, assuming intelligence is computational, is equivalent to that of solving the central artificial intelligence problem—making computers as intelligent as people, or strong AI. To call a problem AI-complete reflects an attitude that it would not be solved by a simple specific algorithm.
Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence.
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, causal inference, etc.
Sokoban is a puzzle video game in which the player pushes boxes around in a warehouse, trying to get them to storage locations. The game was designed in 1981 by Hiroyuki Imabayashi, and first published in December 1982.
In computer science and artificial intelligence, combinatorial search studies search algorithms for solving instances of problems that are believed to be hard in general, by efficiently exploring the usually large solution space of these instances. Combinatorial search algorithms achieve this efficiency by reducing the effective size of the search space or employing heuristics. Some algorithms are guaranteed to find the optimal solution, while others may only return the best solution found in the part of the state space that was explored.
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research focusing on the resolution of particular forms of the constraint satisfaction problem.
Intelligence has been defined in many ways: the capacity for abstraction, logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, critical thinking, and problem-solving. It can be described as the ability to perceive or infer information; and to retain it as knowledge to be applied to adaptive behaviors within an environment or context.
An artificial general intelligence (AGI) is a hypothetical type of intelligent agent which, if realized, could learn to accomplish any intellectual task that human beings or animals can perform. Alternatively, AGI has been defined as an autonomous system that surpasses human capabilities in the majority of economically valuable tasks.Creating AGI is a primary goal of some artificial intelligence research and of companies such as OpenAI, DeepMind, and Anthropic. AGI is a common topic in science fiction and futures studies.
In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, tune, or select a heuristic that may provide a sufficiently good solution to an optimization problem or a machine learning problem, especially with incomplete or imperfect information or limited computation capacity. Metaheuristics sample a subset of solutions which is otherwise too large to be completely enumerated or otherwise explored. Metaheuristics may make relatively few assumptions about the optimization problem being solved and so may be usable for a variety of problems.
Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component with a learning component. Learning classifier systems seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions. This approach allows complex solution spaces to be broken up into smaller, simpler parts.
In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point in the feasible region.
Insight is the understanding of a specific cause and effect within a particular context. The term insight can have several related meanings:
Automated planning and scheduling, sometimes denoted as simply AI planning, is a branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent agents, autonomous robots and unmanned vehicles. Unlike classical control and classification problems, the solutions are complex and must be discovered and optimized in multidimensional space. Planning is also related to decision theory.
A physical symbol system takes physical patterns (symbols), combining them into structures (expressions) and manipulating them to produce new expressions.
The blocks world is a planning domain in artificial intelligence. The algorithm is similar to a set of wooden blocks of various shapes and colors sitting on a table. The goal is to build one or more vertical stacks of blocks. Only one block may be moved at a time: it may either be placed on the table or placed atop another block. Because of this, any blocks that are, at a given time, under another block cannot be moved. Moreover, some kinds of blocks cannot have other blocks stacked on top of them.
God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It refers to any algorithm which produces a solution having the fewest possible moves. The allusion to the deity is based on the notion that an omniscient being would know an optimal step from any given configuration.
A hyper-heuristic is a heuristic search method that seeks to automate, often by the incorporation of machine learning techniques, the process of selecting, combining, generating or adapting several simpler heuristics to efficiently solve computational search problems. One of the motivations for studying hyper-heuristics is to build systems which can handle classes of problems rather than solving just one problem.
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