Linear-time version of Holub's algorithm for morphic imprimitivity testing
نویسندگان
چکیده
منابع مشابه
Linear-Time Version of Holub's Algorithm for Morphic Imprimitivity Testing
Stepan Holub (Discr. Math., 2009) gave the first polynomial algorithm deciding whether a given word is a nontrivial fixed point of a morphism. His algorithm works in quadratic time for large alphabets. We improve the algorithm to work in linear time. Our improvement starts with a careful choice of a subset of rules used in Holub’s algorithm that is necessary to grant correctness of the algorith...
متن کاملComplexity of testing morphic primitivity
The word u = abaaba satisfies f(u) = u where f maps b to aba and cancels a. Such words, which are fixed points of a nontrivial morphism, are called morphically imprimitive. On the other hand, the word u′ = abba can be easily verified to be morphically primitive, which means that the only morphism satisfying f(u′) = u′ defined on {a, b}∗ is the identity. Fixed points of word morphisms and morphi...
متن کاملAN ALGORITHM FOR FINDING THE STABILITY OF LINEAR TIME-INVARIANT SYSTEMS
The purpose of this paper is to show that the ideas and techniques of the classical methods of finding stability, such as the criteria of Leonhard and Nyquist, can be used to derive simple algorithm to verify stability. This is enhanced by evaluating the argument of the characteristic equation of a linear system in the neighbourhood of the origin of the complex plane along the imaginary axis
متن کاملEigenvalues and Transduction of Morphic Sequences: Extended Version
We study finite state transduction of automatic and morphic sequences. Dekking [4] proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in the proof to show that non-erasing transductions preserve a condition called α-substitutivity. Roughly, a sequence is α-substitutive if the sequence can...
متن کاملImplementation of the algorithm for testing an automaton for synchronization in linear expected time
Berlinkov has suggested an algorithm that, given a deterministic finite automaton A, verifies whether or not A is synchronizing in linear (of the number of states and letters) expected time. We present a modification of Berlinkov’s algorithm which we have implemented and tested. Our experiments show that the implementation outperforms the standard quadratic algorithm even for automata of modest...
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: Theoretical Computer Science
سال: 2015
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.07.055