scholarly journals Relationships between the Chicken McNugget Problem, Mutations of Brauer Configuration Algebras and the Advanced Encryption Standard

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1937
Author(s):  
Agustín Moreno Moreno Cañadas ◽  
Isaías David Marín Marín Gaviria ◽  
Juan David Camacho Camacho Vega
Keyword(s):  
Diophantine Equations ◽  
Finite Automata ◽  
Advanced Encryption Standard ◽  
Deterministic Finite Automata ◽  
Key Schedule

Mutations on Brauer configurations are introduced and associated with some suitable automata to solve generalizations of the Chicken McNugget problem. Additionally, based on marked order polytopes, the new Diophantine equations called Gelfand–Tsetlin equations are also solved. The approach allows algebraic descriptions of some properties of the AES key schedule via some Brauer configuration algebras and suitable non-deterministic finite automata (NFA).

Deterministic finite automata with recursive calls and DPDAs

2003 ◽  
Vol 87 (4) ◽  
pp. 187-193
Author(s):  
Jean H. Gallier ◽  
Salvatore La Torre ◽  
Supratik Mukhopadhyay
Keyword(s):  
Finite Automata ◽  
Deterministic Finite Automata

The detection and stabilisation of limit cycle for deterministic finite automata

2017 ◽  
Vol 91 (4) ◽  
pp. 874-886 ◽  
Author(s):  
Xiaoguang Han ◽  
Zengqiang Chen ◽  
Zhongxin Liu ◽  
Qing Zhang
Keyword(s):  
Limit Cycle ◽  
Finite Automata ◽  
Deterministic Finite Automata

Space-bounded OTMs and REG ∞

Computability ◽  
2021 ◽  
pp. 1-16
Author(s):  
Merlin Carl
Keyword(s):  
Complexity Theory ◽  
Turing Machine ◽  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Logarithmic Space ◽  
Working Space ◽  
Important Theorem

An important theorem in classical complexity theory is that REG = LOGLOGSPACE, i.e., that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs) and show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA, which is a transfinite analogue of LOGLOGSPACE ⊆ REG; the other direction, however, is easily seen to fail.

scholarly journals New Results on Vector and Homing Vector Automata

2019 ◽  
Vol 30 (08) ◽  
pp. 1335-1361
Author(s):  
Özlem Salehi ◽  
Abuzer Yakaryılmaz ◽  
A. C. Cem Say
Keyword(s):  
Real Time ◽  
Nonnegative Integer ◽  
Diophantine Equations ◽  
Finite Automata ◽  
Separation Problem ◽  
Integer Solutions ◽  
Homing Vector

We present several new results and connections between various extensions of finite automata through the study of vector automata and homing vector automata. We show that homing vector automata outperform extended finite automata when both are defined over [Formula: see text] integer matrices. We study the string separation problem for vector automata and demonstrate that generalized finite automata with rational entries can separate any pair of strings using only two states. Investigating stateless homing vector automata, we prove that a language is recognized by stateless blind deterministic real-time version of finite automata with multiplication iff it is commutative and its Parikh image is the set of nonnegative integer solutions to a system of linear homogeneous Diophantine equations.

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