Practical decomposition of automata
TLDR
A series-parallel decomposition of an automaton A into r components is said to be practical if every component has fewer states than the original automaton C iff the product of the numbers of states of components is equal to the number ofStates of A.Abstract:
A series-parallel decomposition of an automaton A into r components ( r ⩾ 1) is said to be practical if every component has fewer states than the original automaton A . It is said to be perfect iff the product of the numbers of states of components is equal to the number of states of A . Necessary and sufficient conditions are given for a Moore-type automaton to have a practical decomposition. An algebraic criterion is also given for a reduced, strongly connected permutation automaton to have a perfect decomposition. It should be noted that an automaton may have a perfect decomposition although its semigroup is a simple group, and that an automaton may not have a practical decomposition, while its semigroup is a nonsimple group.read more
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Book ChapterDOI
The Algebraic Theory of Automata
TL;DR: The aim of this chapter is to introduce the reader to the theory of discrete information processing systems (automata) and to develop an algebraic framework within which to talk about their complexity.
Posted Content
Cascade Product of Permutation Groups
TL;DR: In this article, the cascade product of permutation groups is defined as an external product, an explicit construction of substructures of the iterated wreath product that are much smaller than the full Wreath product.
Journal ArticleDOI
Automated semantics-preserving parallel decomposition of finite component and connector architectures
TL;DR: A concept of influence between channels of components is presented that supports automated semantics-preserving parallel decomposition of finite deterministic component implementations into independent, more comprehensible components that are better accessible for analysis and development.
Journal ArticleDOI
Decomposition and factorization of chemical reaction transducers
Fumiya Okubo,Takashi Yokomori +1 more
TL;DR: For factorization, it is shown that each CRT T can be realized in the form: T ( x) = g ( h − 1 ( x ) ∩ L ) for some codings g, h and a chemical reaction language L, which provides a generalization of Nivat's Theorem for rational transducers.
Proceedings ArticleDOI
Data flow algorithms for processors with vector extensions: Handling actors with internal state
TL;DR: This paper proposes a methodology for using the parallel scan (also known as prefix sum) pattern to create algorithms for multiple simultaneous invocations of such an actor that results in vectorizable code.
References
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Book
The theory of groups
TL;DR: The theory of normal subgroups and homomorphisms was introduced in this article, along with the theory of $p$-groups regular $p-groups and their relation to abelian groups.