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### Automata, Boolean Matrices, and Ultimate Periodicity

Guo-Qiang Zhang
1999 Information and Computation
A new characterization of such functions is derived in terms of the property of ultimate periodicity with respect to powers of Boolean matrices.  ...  This paper presents a Boolean-matrix-based method to automata theory, with an application to the study of regularity-preserving functions.  ...  Rod Canfield got me interested in regularity-preserving functions in the first place thanks for letting me teach automata theory again and again, each time irritated by questions about regularity-preserving  ...

### Rational Transformations of Formal Power Series [chapter]

Manfred Droste, Guo-Qiang Zhang
2001 Lecture Notes in Computer Science
Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines.  ...  In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series.  ...  The previous two lemmata and Theorems 2.1 and 3.2 lead to the following theorem. (1) f is ultimately periodic with respect to K-matrices. (2) f −1 preserves recognizability for S ∈ K {a} * . (3) the amplifying  ...

### On transformations of formal power series

Manfred Droste, Guo-Qiang Zhang
2003 Information and Computation
Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines.  ...  In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series.  ...  A main result in  is that a function f : N → N is regularity preserving if and only if it is ultimately periodic (see Definition 4.1) with respect to Boolean matrices.  ...

### Page 1969 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews
{For the entire collection see MR 2000k:05006. } 2001¢:68088 68Q45 03D05 Zhang, Guo-Qiang (1-GA-C; Athens, GA) Automata, Boolean matrices, and ultimate periodicity.  ...  A new characterization of such functions is derived in terms of the property of ultimate periodicity with re- spect to powers of Boolean matrices.  ...

### CONCATENATION AND KLEENE STAR ON DETERMINISTIC FINITE AUTOMATA

GUO-QIANG ZHANG, XIANGNAN ZHOU, ROBERT FRASER, LICONG CUI
2012 Quantitative Logic and Soft Computing
Automata, Boolean matrices, and ultimate periodicity.  ...  Laws of Boolean matrices capture language operations inductively and algebraically.  ...

### Abstracts of Current Computer Literature

1969 IEEE transactions on computers
W-Machine Assembler and Simulationsee 6938. Synchronization and General Repetitive Machines, with Applications to Ultimate Definite Automata, B. G. Reynolds and W. F.  ...  Bandit Problems 6944 Type 3 Languages 6900 U Ultimate Definite Automata 6906 Unambiguity 6900 Unate Cellular Arrays 6896 Unateness of Boolean Functions 6895 Unidirectional Shift Registers 6908  ...

### Some considerations on fuzzy automata

Masaharu Mizumoto, Junichi Toyoda, Kohkichi Tanaka
1969 Journal of computer and system sciences (Print)
The fuzzy sets of input sequences characterized by fuzzy automata constitute a distributive lattice, and the complement of the fuzzy set can be characterized by an optimistic fuzzy automaton.  ...  In this paper, we show: The threshold of fuzzy automata can be changed arbitrarily.  ...  ACKNOWLEDGMENT The authors gratefully acknowledge the suggestions and criticisms of the members of Prof. Tanaka's Lab.  ...

### Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Carlo Mereghetti, Beatrice Palano, Giovanni Pighizzini
2001 RAIRO - Theoretical Informatics and Applications
Moreover, we exhibit one-way quantum finite automata that, for any m, accept Lm with isolated cut point and only two states.  ...  These results are settled within a survey on unary automata aiming to compare the descriptional power of deterministic, nondeterministic, probabilistic and quantum paradigms.  ...  To emphasize the periodicity of a language L as in Theorem 1.1, we say that L is ultimately χ-cyclic.  ...

### Sequential simulation of parallel iterations and applications

Maurice Tchuente
1986 Theoretical Computer Science
This result is used to unify and generalize some results on the dynamic behaviour of finite automata networks. R~sum~.  ...  We first show that the parallel evolution of a network of automata N can be sequentially simulated by another network N' whose local transition functions are the same as those of N.  ...  sequence is ultimately periodic, i.e., there exist two integers P (the cycle length or period), and T (the transient length) such that x°=(_O, _l)->x' =(1,_l)~x 2=(_0,_0)~x3=(_1, _O)~x4=(O, 1)=x °. x'  ...

### A Hierarchical Classification of First-Order Recurrent Neural Networks [chapter]

Jérémie Cabessa, Alessandro E. P. Villa
2010 Lecture Notes in Computer Science
This classification is achieved by proving an equivalence result between such neural networks and deterministic Büuchi automata, and then translating the Wadge classification theory from the abstract machine  ...  The obtained hierarchy of neural networks is proved to have width 2 and height ω + 1, and a decidability procedure of this hierarchy is provided.  ...  ···, s K (t)) are boolean vectors, A, B, and c are rational matrices of sizes N × N, N × K, and N × 1, respectively, and σ denotes the classical hard threshold activation function applied component by  ...

### Abstracts of Current Computer Literature

1970 IEEE transactions on computers
A class of Boolean functions arising naturally from a consideration of the periodicities of multithreshold functions is defined and the basic properties of these functions, the completely periodic functions  ...  Error 8048 Algebra; Algebraic Algebraic Properties of Partially Separable Switching Functions 7983 -see also Algebraic Equations, Automata, Boolean, Matrices, Polynomials, Sequen- tial Machines  ...

### Abstracts of Current Computer Literature

1970 IEEE transactions on computers
7944 The Use of Boolean Transition Matrices in Compiling, H.  ...  It is shown that the latter situation is the exception, the former the rule: the only sets recognizable independently of base are those that are ultimately periodic; others, if recognizable at all, are  ...

### Logics of Finite Hankel Rank [chapter]

2015 Lecture Notes in Computer Science
We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the Feferman-Vaught Theorem.  ...  Kotek for letting us use his example, and for valuable discussions.  ...  Then M A has finite Boolean rank iff A is ultimately periodic. Theorem 1. Let τ graphs be the vocabulary with one binary edge-relation, and τ 1 be τ graphs augmented by one vertex label.  ...

### Abstracts of Current Computer Literature

1969 IEEE transactions on computers
Formal Systems for Algebraic Transfor- mation of Regular Expressions 6357 -see also Algebraic Equations, Automata, Boolean, Matrices, Sequential Algebraic Equations Solution of Linear Algebraic Equations  ...  SYSTRAN was originally developed around a data acquisition system and was primarily intended for use in analysis of periodic and transient data.  ...

### Algorithmic Problems in Group Theory (Dagstuhl Seminar 19131)

Volker Diekert, Olga Kharlampovich, Markus Lohrey, Alexei Myasnikov, Michael Wagner
2019 Dagstuhl Reports
On one hand, groups played an important rule in many developments in complexity theory and automata theory.  ...  In the last 20 years we have seen many new successful interactions between group theory and computer science.  ...  If A is in fact a subset of N (meaning only non-negative powers of q have non-zero coefficients), then this is well-known to be true: Every submonoid of N is ultimately periodic and thus automatic (and  ...
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