Planning and Learning in Permutation Groups

Planning is defined as the problem of synthesizing a desired behavior from given basic operations, and learning is defined as the dual problem of analyzing a given behavior to determine the unknown basic operations. Algorithms for solving these problems in the context of invertible operations on finite-state environments are developed. In addition to their obvious artificial intelligence applications, the algorithms can efficiently find the shortest way to solve Rubik's cube, test ping-pong protocols, and solve systems of equations over permutation groups. >

Authors

• Amos Fiat
• Shahar Moses
• Adi Shamir
• Ilan Shimshoni
• Gábor Tardos

Keywords

• Intelligent robots
• Artificial intelligence
• System testing
• Protocols
• Equations
• Polynomials
• Pediatrics
• Mathematics
• Vectors
• Permutation Group
• Time And Space
• Learning Algorithms
• System Of Equations
• Algebra
• Time Complexity
• Reduction Process
• Learning Problem
• Exhaustive Search
• Proportionality Constant
• Correction Algorithm
• Space Complexity
• Linear Time
• Word Length
• Vertices
• Applied Maths
• Substring
• Problem Representation
• Lexicographic
• Pair Of Vertices