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REPORTS > KEYWORD > GROUP THEORY:
Reports tagged with Group Theory:
TR01-040 | 16th May 2001

#### On the Languages Recognized by Nilpotent Groups (a translation of "Sur les Langages Reconnus par des Groupes Nilpotents")

We study a model of computation where executing a program on an input corresponds to calculating a product in a finite monoid. We show that in this model, the subsets of {0,1}^n that can be recognized by nilpotent groups have exponential cardinality.

Translator's note: This is a translation of the ... more >>>

TR01-067 | 18th September 2001
Hubie Chen

#### Polynomial Programs and the Razborov-Smolensky Method

Representations of boolean functions as polynomials (over rings) have
been used to establish lower bounds in complexity theory. Such
representations were used to great effect by Smolensky, who
established that MOD q \notin AC^0[MOD p] (for distinct primes p, q)
by representing AC^0[MOD p] functions as low-degree multilinear
polynomials over ... more >>>

TR10-051 | 26th March 2010