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 selfdelimiting 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 2 G. J. Chaitin properties of the entropy concept of information theory. For example, H(A;B) = H(A) + H(B=A) + O(1). Also, if a program of length k is assigned measure 2 \Gammak , then H(A) = \Gamma log 2 (the probability that the standard universal computer will calculate A) +O(1). Key Words and Phrases: computational complexity, entropy, information theory, instantaneous code, Kraft inequality, minimal program, probab...

In this paper, we first introduce minimal, maximal and weighted disclosure risk measures for microaggregation disclosure control method. Our disclosure risk measures are more applicable to reallife situations, compute the overall disclosure risk, and are not linked to a target individual. After defining those disclosure risk measures, we then introduce an information loss measure for microaggregation. The minimal disclosure risk measure represents the percentage of records, which can be correctly identified by an intruder based on prior knowledge of key attribute values. The maximal disclosure risk measure considers the risk associated with probabilistic record linkage for records that are not unique in the masked microdata. The weighted disclosure risk measure allows the data owner to compute the risk of disclosure based on weights associated with different clusters of records. Information loss measure, introduced in this paper, extends the existing measure proposed by Domingo-Ferrer, and captures the loss of information at record level as well as from the statistical integrity point of view. Using simulated medical data in our experiments, we show that the proposed disclosure risk and information loss measures perform as expected in real-life situations..