TY - JOUR
AU1 - Chaitin, Gregory J.
AB -  A Theory of Program Size Formally Identical to Information Theory GREGORY J. CHAITIN I B M Thomas J. Watson Research Center, Yorktown Heights, New York ABSTRACT. A new definition of program-size complexity is made. H(A,B/C,D) is defined to be the size in bits of the shortest self-delimiting program for calculating strings A and B if one is given a minimal-size self-delimiting program for calculating strings C and D. This differs from previous definitions: (1) programs are required to be self-delimiting, i.e. no program is a prefix of another, and (2) instead of being given C and D directly, one is given a program for calculating them that is minimal in size. Unlike previous definitions, this one has precisely the formal properties of the entropy concept of information theory. For example, H(A,B) = H(A) + H ( B / A ) -~ 0(1). Also, if a program of length k is assigned measure 2-k, then H(A) = -log2 (the probability that the standard universal computer will calculate A) -{- 0(1). PHRASES: computational complexity, entropy, information theory, instantaneous code, Kraft inequality, minimal program, probability theory, program size, random string, reeursive f u n c t i o n theory, Turing 
TI - A Theory of Program Size Formally Identical to Information Theory
JF - Journal of the ACM (JACM)
DO - 10.1145/321892.321894
DA - 1975-07-01
UR - https://www.deepdyve.com/lp/association-for-computing-machinery/a-theory-of-program-size-formally-identical-to-information-theory-AMeKRP188V
SP - 329
VL - 22
IS - 3
DP - DeepDyve
ER -