When there are several versions of a name, I normally use the one that was current closest to the time of work I mention.

Various forms of Boolean minimization have routinely been used in chip and circuit design since the late 1980s, though often physical and geometrical constraints are now more important than pure logical ones.

Polymers whose lengths differ by more than one or two repeating units often seem to smell different, and it is conceivable that elaborate general features of shapes of molecules can be perceived.

One could in principle imagine defining mathematics to encompass all studies of abstract systems, and indeed this was in essence the definition that I had in mind when I chose the name Mathematica.

Note that by using RotateLeft and RotateRight one automatically gets cyclic boundary conditions.

But in any given language there are always many exceptions, and in the end it has proved essentially impossible to identify specific detailed features—beyond for example the existence of nouns and verbs—that are convincingly universal across more than just languages with clear historical connections (such as the Indo-European ones). (One obvious general deviation from the context-free model is that in practice subordinate clauses can never be nested too deep if a sentence is expected to be understood.)

One mathematically convenient but probably unrealistic model studied in recent years in the context of computational learning theory involves building up minimal Boolean formulas consistent with the examples seen.

One-element-dependence tag systems [emulating TMs] Writing the rule {3, {{0, _, _}  {0, 0}, {1, _, _}  {1, 1, 0, 1}}} from page 895 as {3, {0  {0, 0}, 1  {1, 1, 0, 1}}} the evolution of a tag system that depends only on its first element is obtained from TS1EvolveList[rule_, init_, t_] := NestList[TS1Step[rule, #] &, init, t] TS1Step[{n_, subs_}, {}] = {} TS1Step[{n_, subs_}, list_] := Drop[Join[list, First[list] /. subs], n] Given a Turing machine in the form used on page 888 the following will construct a tag system that emulates it: TMToTS1[rules_] := {2, Union[Flatten[rules /.

But even though millions of discrete samples are now used, each one typically still represents something much larger then for example a single cloud.

And indeed the kinds of proofs normally considered most mathematically valuable are ones that get built up in terms of concepts and constructs that are somehow expected to be as generally applicable as possible.