The Krohn-Rhodes Theorem and Local Divisors
نویسندگان
چکیده
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.
منابع مشابه
An Effective Lower Bound for Group Complexity of Finite Semigroups and Automata
The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, Complexity of finite semigroups, Annals of Mathematics (2) 88 (1968), 128–160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, Algebraic theory of machines, I: Prime decomposition theorem for finite semigroups and machines, Transactions of the Ameri...
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 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 کاملSix lectures on algebraic theory of automata
Introduction . 1 Lecture 1. Seraiautomata and Automata . , 3 Lecture 2. Coverings and Homomorphisms of Automata 8 Lecture 3. Covering by Direct and Cascade Products of Semiautomata 15 Lecture 4. Permutation and Reset Semiautomata 24 Lecture 5. The Structure Theorem of Krohn and Rhodes . . . .31 Lecture 6. The Necessity of Certain Components in a Cascade Product Covering of a Semiautomaton . . ....
متن کاملFinite semigroups, feedback, and the Letichevsky criteria on non-empty words in finite automata
ON NON-EMPTY WORDS IN FINITE AUTOMATA PÁL DÖMÖSI, CHRYSTOPHER L. NEHANIV, AND JOHN L. RHODES ABSTRACT. This paper relates classes of finite automata under various feedback products to some well-known pseudovarieties of finite semigroups via a study of their irreducible divisors (in the sense of Krohn-Rhodes). In particular, this serves to relate some classical results of Krohn, Rhodes, Stiffler...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Fundam. Inform.
دوره 116 شماره
صفحات -
تاریخ انتشار 2012