the first wave was much closer to the matrix multiplication circejerk that is now in force today
https://sci-hub.red/storage/moscow/1854/aa5e8e92676bc6e1f7c540b1861796a5/gill1977.pdf
COMPUTATIONAL COMPLEXITY OF PROBABILISTIC TURING MACHINES *
what's the asterisk this time?
Received by the editors June 1, 1976, and in revised form February 18, 1977.
backdating. it's for backdating
4. An example of probabilistic speedup.
the terminology is completely unchanged. "quantum advantage. quantum supremacy"
A probabilistic machine recognizes a language if the machine computes the characteristic function of the language.
here you can see precisely how chomsky's "formal languages" grift was always intended to serve the rankest "AI" propaganda
(i) PP is the class of languages recognized by polynomial
bounded PTMs.
the prime number boys are obsessed with their own penis
(ii) BPP is the class of languages recognized by polynomial bounded PTMs with bounded error probability.
i think this one was actually the most shrewd, because it took a concept like "bounded error" which has meaning in REAL ACTUAL SCIENCE BY SCIENTISTS and moved into the asymptotic realm which has meaning in REAL ACTUAL MATHEMATICS DONE BY MATHEMATICIANS. unfortunately very clever of them
(iii) ZPP is the class of languages recognized by PTMs with polynomial bounded average run time and zero error probability.
they never mention this again except to say
We can suggest no language in ZPP
before, again, mentioning prime number factorization shit