Category Archives: Quantifying Structure

   What does it mean to say that one thing is more complex than another? Like most words,"complexity" has many meanings. In Chapter 1 we briefly discussed the "complexity" ofcomputation — of problems and algorithms. In this chapter we will … Continue reading →

   It is natural to define a random sequence as one which has no statistical regularities (vonMises, 1957). For instance, one might propose that in a random binary sequence 1 should occurexactly as often as 0. Also, one might require … Continue reading →

   Charles S. Peirce, the turn-of-the-century American philosopher, liked to talk about the "onelaw of mind." He gave this law many different formulations, the most suggestive of which wasonly five words: "the tendency to take habits". This simple, potent idea … Continue reading →

   Koppel [8] has recently proposed an alternative to the KCS complexity measure. According toKoppel’s measure, the sequences which are most complex are not the structureless ones. Neither,of course, are they the ones with very simple structures, like 00000000000…. Rather, … Continue reading →

   We have discussed several different measures of static complexity, which measure ratherdifferent things. But all these measures have one thing in common: they work by singling out theone pattern which minimizes some quantity. It is equally interesting to study … Continue reading →