scholarly journals Finite Automata Presentable Abelian Groups

Author(s):  
André Nies ◽  
Pavel Semukhin
2009 ◽  
Vol 161 (3) ◽  
pp. 458-467 ◽  
Author(s):  
André Nies ◽  
Pavel Semukhin

Author(s):  
Y.S. Gan ◽  
W.H. Fong ◽  
N.H. Sarmin ◽  
S. Turaev

One of the classic models of automata is finite automata, which determine whether a string belongs to a particular language or not. The string accepted by automata is said to be recognized by that automata. Another type of automata, so-called Watson-Crick automata, with two reading heads that work on double-stranded tapes using the complimentary relation. Finite automata over groups extend the possibilities of finite automata and allow studying the properties of groups using finite automata. In this paper, we consider finite automata over some Abelian groups ℤn and ℤn × ℤn. The relation of Cayley table to finite automata diagram is introduced in the paper. Some properties of groups ℤn and ℤn × ℤn in terms of automata are also presented in this paper.


2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.


2017 ◽  
Vol 5 (1) ◽  
pp. 8-15
Author(s):  
Sergii Hilgurt ◽  

The multi-pattern matching is a fundamental technique found in applications like a network intrusion detection system, anti-virus, anti-worms and other signature- based information security tools. Due to rising traffic rates, increasing number and sophistication of attacks and the collapse of Moore’s law, traditional software solutions can no longer keep up. Therefore, hardware approaches are frequently being used by developers to accelerate pattern matching. Reconfigurable FPGA-based devices, providing the flexibility of software and the near-ASIC performance, have become increasingly popular for this purpose. Hence, increasing the efficiency of reconfigurable information security tools is a scientific issue now. Many different approaches to constructing hardware matching circuits on FPGAs are known. The most widely used of them are based on discrete comparators, hash-functions and finite automata. Each approach possesses its own pros and cons. None of them still became the leading one. In this paper, a method to combine several different approaches to enforce their advantages has been developed. An analytical technique to quickly advance estimate the resource costs of each matching scheme without need to compile FPGA project has been proposed. It allows to apply optimization procedures to near-optimally split the set of pattern between different approaches in acceptable time.


2009 ◽  
Vol 18 (1) ◽  
pp. 145-158
Author(s):  
Jiang Zhang ◽  
Keyword(s):  

Author(s):  
Bodan Arsovski

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.


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