Results 31 to 40 of about 210,069 (312)
Automatic Sequences and Generalised Polynomials [PDF]
Canadian Journal of Mathematics, 2019 AbstractWe conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic.Using methods from ergodic theory, we are able to partially resolve this conjecture, proving that any hypothetical counterexample is periodic away from a very sparse and structured set.
Byszewski, Jakub, Konieczny, Jakub
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Rigorous Simulation-Based Automatic Identification of the Optimal Separation Sequence
Chemical Engineering Transactions, 2020 Separation sequence optimization is an energy-saving strategy for improving the process economy. This work introduces a rigorous simulation-based method to identify the best separation sequence for the separation of N-component mixture, aiming to reduce ...
Dan Zhang +4 more
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Transduction of Automatic Sequences and Applications
, 2023 We consider the implementation of the transduction of automatic sequences, and their generalizations, in the Walnut software for solving decision problems in combinatorics on words. We provide a number of applications, including (a) representations of n! as a sum of three squares (b) overlap-free Dyck words and (c) sums of Fibonacci representations. We
Jeffrey O. Shallit, Anatoly Zavyalov
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Towards Automatic Design of Reflective Optical Systems
Advanced Photonics Research, 2023 Traditional optical design processes can only obtain a few design solutions after a time‐consuming trial‐and‐error process. During this process, how to select the numbers and sequence of surfaces of different types (spherical, aspherical, and freeform ...
Xinyu Liu, Jun Zhu
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An integrated search-based approach for automatic testing from extended finite state machine (EFSM) models [PDF]
, 2011 This is the post-print version of the Article - Copyright @ 2011 ElsevierThe extended finite state machine (EFSM) is a modelling approach that has been used to represent a wide range of systems.
Stephen Swift +5 more
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On the Final Coalgebra of Automatic Sequences [PDF]
, 2012 Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer science; and they appear in mathematics in many different ways ...
Clemens Kupke, Jan J. M. M. Rutten
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On the automaticity of the Hankel determinants of a family of automatic sequences [PDF]
Theoretical Computer Science, 2019 Hankel determinants and automatic sequences are two classical subjects widely studied in Mathematics and Theoretical Computer Science. However, these two topics were considered totally independently, until in 1998, when Allouche, Peyrière, Wen and Wen proved that all the Hankel determinants of the Thue-Morse sequence are nonzero.
Yining Hu, Guoniu Wei-Han
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Repetition factorization of automatic sequences
CoRR, 2023 Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several (generalized) automatic sequences, including the infinite Fibonacci word, the Thue-Morse word, paperfolding words, and ...
Jeffrey O. Shallit, Xinhao Xu
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BMC Bioinformatics, 2005 Background Structure-dependent substitution matrices increase the accuracy of sequence alignments when the 3D structure of one sequence is known, and are successful e.g. in fold recognition. We propose a new automated method, EvDTree, based on a decision
Gracy Jérôme +2 more
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Frobenius Numbers and Automatic Sequences
CoRR, 2021 The Frobenius number $g(S)$ of a set $S$ of non-negative integers with $\gcd 1$ is the largest integer not expressible as a linear combination of elements of $S$. Given a sequence ${\bf s} = (s_i)_{i \geq 0}$, we can define the associated sequence $G_{\bf s} (i) = g(\{ s_i,s_{i+1},\ldots \})$. In this paper we compute $G_{\bf s} (i)$ for some classical
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