Efficient programs of NPC problems should be length upper-bounded, and a thought experiment to search for them by machine enumeration

This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: • On Universal Turing Machines, a program’s time complexity should be characterized as: execution time(n) = loading time(n) + running time(n). • Introduces the concept of bounded algorithms; proposes a comparison based criterion to decide if a bounded algorithm is inefficient; and establishes the length upper bound of efficient bounded programs. • Introduces the growth rate characteristic function to evaluate program complexity, which is more easily machine checkable based on observations. • Raises the theoretical question: if there exists any bounded algorithm with polynomial execution time for NPC problems.