Krohn-Rhodes complexity pseudovarieties are not finitely based
نویسندگان
چکیده
منابع مشابه
Krohn-Rhodes complexity pseudovarieties are not finitely based
We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most n is not finitely based for all n > 0. More specifically, for each pair of positive integers n, k, we construct a monoid of complexity n+1, all of whose k-generated submonoids have complexity at most n. Mathematics Subject Classification. 20M07.
متن کاملThe Krohn-Rhodes Theorem and Local Divisors
We give a new proof of the Krohn-Rhodes theorem using local divisors. The proof provides nearly as good a decomposition in terms of size as the holonomy decomposition of Eilenberg, avoids induction on the size of the state set, and works exclusively with monoids with the base case of the induction being that of a group.
متن کاملOn the Krohn-Rhodes Cascaded Decomposition Theorem
The Krohn-Rhodes theorem states that any deterministic automaton is a homomorphic image of a cascade of very simple automata which realize either resets or permutations. Moreover, if the automaton is counter-free, only reset automata are needed. In this paper we give a very constructive proof of a variant of this theorem due to Eilenberg.
متن کاملOn the Krohn-rhodes Complexity of Semigroups of Upper Triangular Matrices
We consider the Krohn-Rhodes complexity of certain semigroups of upper triangular matrices over finite fields. We show that for any n > 1 and finite field k, the semigroups of all n × n upper triangular matrices over k and of all n × n unitriangular matrices over k have complexity n− 1. A consequence is that the complexity c > 1 of a finite semigroup places a lower bound of c+1 on the dimension...
متن کاملMerge decompositions, two-sided Krohn-Rhodes, and aperiodic pointlikes
This paper provides short proofs of two fundamental theorems of finite semigroup theory whose previous proofs were significantly longer, namely the two-sided Krohn-Rhodes decomposition theorem and Henckell's aperiodic pointlike theorem, using a new algebraic technique that we call the merge decomposition. A prototypical application of this technique decomposes a semigroup $T$ into a two-sided s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 2005
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita:2005016