Large Aperiodic Semigroups

We search for the largest syntactic semigroups of star-free languages having n left quotients; equivalently, we look for the largest transition semigroups of aperiodic finite automata with n states. We first introduce unitary semigroups generated by transformations that change only one state. In particular, we study unitary-complete semigroups which have a special structure, and show that each maximal unitary semigroup is unitary-complete. For [Formula: see text] we exhibit a unitary-complete semigroup that is larger than any aperiodic semigroup known to date. We then present even larger aperiodic semigroups, generated by transformations that map a non-empty subset of states to a single state; we call such transformations and semigroups semiconstant. We examine semiconstant tree semigroups which have a structure based on full binary trees. The semiconstant tree semigroups are at present the best candidates for largest aperiodic semigroups.

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ON THE TRANSITION SEMIGROUPS OF CENTRALLY LABELED RAUZY GRAPHS

International Journal of Algebra and Computation ◽

10.1142/s021819671250018x ◽

2012 ◽

Vol 22 (02) ◽

pp. 1250018 ◽

Cited By ~ 3

Author(s):

JORGE ALMEIDA ◽

ALFREDO COSTA

Keyword(s):

Inverse Limit ◽

Transition Semigroup ◽

Regular Elements ◽

Aperiodic Semigroup ◽

Transition Semigroups ◽

Partial Semigroups

Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. An inverse limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this inverse limit is isomorphic, as a partial semigroup, to the [Formula: see text]-class associated to it in the free pro-aperiodic semigroup.

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A novel cryptosystem based on abstract automata and Latin cubes

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2015.52.2.1309 ◽

2015 ◽

Vol 52 (2) ◽

pp. 221-232

Author(s):

Pál Dömösi ◽

Géza Horváth

Keyword(s):

Block Cipher ◽

Finite Automata ◽

Theoretical Background ◽

Point Of View ◽

Theoretical Point ◽

Transition Matrices ◽

Encryption And Decryption ◽

Secret Keys ◽

Automata Network ◽

Fully Functioning

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.

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Gray-Code Ranking and Unranking on Left-Weight Sequences of Binary Trees

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e99.a.1067 ◽

2016 ◽

Vol E99.A (6) ◽

pp. 1067-1074 ◽

Cited By ~ 2

Author(s):

Ro-Yu WU ◽

Jou-Ming CHANG ◽

Sheng-Lung PENG ◽

Chun-Liang LIU

Keyword(s):

Gray Code ◽

Binary Trees

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Parallel Combining Different Approaches to Multi-pattern Matching for Fpga-based Security Systems

Advances in Cyber-Physical Systems ◽

10.23939/acps2020.01.008 ◽

2017 ◽

Vol 5 (1) ◽

pp. 8-15

Author(s):

Sergii Hilgurt ◽

Keyword(s):

Information Security ◽

Pattern Matching ◽

Intrusion Detection System ◽

Detection System ◽

Finite Automata ◽

Network Intrusion Detection ◽

Security Systems ◽

Analytical Technique ◽

Network Intrusion ◽

Pros And Cons

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.

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Modeling and Simulation of Two Geometries of Single State Virtual Impactor

Journal of Chemical Biological and Physical Sciences ◽

10.24214/jcbsc.c.10.2.07275 ◽

2020 ◽

Vol 10 (2) ◽

Keyword(s):

Modeling And Simulation ◽

Virtual Impactor ◽

Single State

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Complexity and Universality of Iterated Finite Automata

Complex Systems ◽

10.25088/complexsystems.18.1.145 ◽

2009 ◽

Vol 18 (1) ◽

pp. 145-158

Author(s):

Jiang Zhang ◽

Keyword(s):

Finite Automata

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NADH in Solution: A Single State

10.26434/chemrxiv.8208407.v1 ◽

2019 ◽

Author(s):

Joachim Hönes ◽

Julia Wack ◽

Katja Schmitz

Keyword(s):

Aqueous Solution ◽

Base Stacking ◽

Spectroscopic Evidence ◽

Single State

<div>Spectroscopic evidence is presented to show that NADH in aqueous solution does not exist as a folded/unfolded equilibrium but as a single state. The molecule is folded but without base stacking between dihydronicotinamide and adenine.<br></div>

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ON THE ISSUE OF THE STRATEGY OF RISK MANAGEMENT OF EMERGENCY SITUATIONS

Collected Scientific Papers of the Institute of Public Administration in the Sphere of Civil Protection ◽

10.35577/iducz.2019.07.07 ◽

2019 ◽

Vol 7 ◽

pp. 72-87

Author(s):

V. Yeliseyev ◽

O. Bondarenko ◽

O. Kovaliov

Keyword(s):

Risk Management ◽

Joint Probability ◽

Scientific Article ◽

Civil Protection ◽

Emergency Situations ◽

Accumulation Of Damage ◽

Single State

The scientific article explores the issues of managing the risks of emergencies in order to improve the readiness and efficiency of the functioning of a single state civil protection system.When calculating the risks, the basic quantitative criteria take into account the probability of emergencies and the magnitude of the damage from these situations.The article presents a method for calculating the joint probability of the action of several emergency factors, taking into account the effect of accumulation of damage.

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