Main Contributions

• Proposes a new logical basis for information theory and probability theory based on computing complexity.
• Redefines the concept of entropy H(x|y) as the minimal length of a program to construct x given y.
• Argues that information theory concepts can be applied to individual values, not just random ones.
• Suggests that randomness can be defined as the absence of periodicity.
• Introduces formulas for information and entropy that incorporate logarithmic-order terms, showing them as approximate equalities rather than exact ones.