Words Guaranteeing Minimum Image

Given a positive integer n and a finite alphabet Σ, a word w over Σ is said to guarantee minimum image if, for every homomorphism φ from the free monoid Σ* over Σ into the monoid of all transformations of an n-element set, the range of the transformation wφ has the minimum cardinality among the ranges of all transformations of the form vφ where v runs over Σ*. Although the existence of words guaranteeing minimum image is pretty obvious, the problem of their explicit description is very far from being trivial. Sauer and Stone in 1991 gave a recursive construction for such a word w but the length of their word was doubly exponential (as a function of n). We first show that some known results of automata theory immediately lead to an alternative construction that yields a simpler word that guarantees minimum image: it has exponential length, more precisely, its length is O(|Σ|(n3-n)). Then with some more effort, we find a word guaranteeing minimum image similar to that of Sauer and Stone but of length O(|Σ|(n2-n)). On the other hand, we prove that the length of any word guaranteeing minimum image cannot be less than |Σ|n-1. © 2004 World Scientific Publishing Company

Words guaranteeing minimal image

Given a positive integer n and a finite alphabet A, a word w over A is said to guarantee minimal image if, for every homomorphism f from the free monoid A* over A into the monoid of all transformations of an n-element set, the range of the transformation wf has the minimum cardinality among the ranges of all transformations of the form vf where v runs over A*. Although the existence of words guaranteeing minimal image is pretty obvious, the problem of their explicit description is very far from being trivial. Sauer and Stone in 1991 gave a recursive construction for such a word w but the length of the word resulting from that construction was doubly exponential (as a function of n). We first show that some known results of automata theory immediately lead to an alternative construction which yields a simpler word that guarantees minimal image: it has exponential length, more precisely, its length is O(|A|^(n^3-n)). Then using a different approach, we find a word guaranteeing minimal image similar to that of Sauer and Stone but of the length O(|A|^(n^2-n)). On the other hand, we observe that the length of any word guaranteeing minimal image cannot be less than |A|^(n-1)

Dimensional Confluence Algebra of Information Space Modulo Quotient Abstraction Relations in Automated Problem Solving Paradigm

Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics defined by alphabetically abstracting net block homomorphism. We obtain minimum prerequisites for the comprehensive connector pairs in a multitude dimensional rewriting closure generating confluence in Participatory algebra for different horizontal and vertical level projections modulo abstraction relations constituting formal semantics for confluence in information space. Participatory algebra with formal automata syntax in its entirety representing automated problem solving paradigm generates rich variety of multitude confluence harmonizers under each fundamental abstraction relation set, horizontal structure mapping and vertical process iteration cardinality.Comment: The current work is an application as a continuation for my previous works in arXiv:1305.5637 and arXiv:1308.5321 using the key definitions of them sustaining consistency, consequently references being minimized. Readers are strongly advised to resort to the mentioned previous works for preliminaries. arXiv admin note: text overlap with arXiv:1408.137

Social Aspects of New Technologies - the CCTV and Biometric (Framing Privacy and Data Protection) in the Case of Poland

The purpose of this paper is to review the institution responsible for the protection of personal data within the European Union and national example - Polish as a country representing the new Member States. The analysis of institutional system - providing legal security of communication and information institutions, companies and citizens against the dangers arising from the ongoing development of innovative new technologies in the European Union and Poland. This article is an attempt to analyze the possibility of using security systems and Biometry CTTV in Poland in terms of legislation. The results of the analysis indicate that, in terms of institutions Poland did not do badly in relation to the risks arising from the implementation of technology. The situation is not as good when it comes to the awareness of citizens and small businesses. This requires that facilitate greater access to free security software companies from data leakage or uncontrolled cyber-terrorist attacks. With regard to the use of security systems, CCTV and biometrics, Poland in legal terms is still early in the process of adapting to EU Directive. The continuous development of technology should force the legislature to establish clear standards and regulations for the application of CCTV technology and biometrics, as it is of great importance in ensuring the fundamental rights and freedoms of every citizen of the Polish Republic.Wyniki analizy wskazują, że pod względem instytucji Polska nie wypada źle w odniesieniu do zagrożeń wynikających z wdrożenia technologii. Sytuacja nie jest tak dobra, jeśli chodzi o świadomość obywateli i mniejszych firm. Wymaga to ułatwiania szerszego dostępu do darmowych programów zabezpieczających firmy przed wyciekiem danych lub niekontrolowanych cyber-ataków terrorystycznych. W odniesieniu do stosowania systemów zabezpieczeń CCTV oraz biometrii, Polska pod względem prawnym jest wciąż na początku procesu dostosowania do dyrektywy UE. Ciągły rozwój technologii powinien zmusić ustawodawcę do stworzenia jednoznacznych standardów i przepisów obowiązujących w zakresie stosowania technologii CCTV oraz biometrii, gdyż ma to ogromne znaczenie w zapewnieniu podstawowych praw i wolności każdego obywatela Rzeczypospolitej Polskiej

Scheduling for Multi-Camera Surveillance in LTE Networks

Wireless surveillance in cellular networks has become increasingly important, while commercial LTE surveillance cameras are also available nowadays. Nevertheless, most scheduling algorithms in the literature are throughput, fairness, or profit-based approaches, which are not suitable for wireless surveillance. In this paper, therefore, we explore the resource allocation problem for a multi-camera surveillance system in 3GPP Long Term Evolution (LTE) uplink (UL) networks. We minimize the number of allocated resource blocks (RBs) while guaranteeing the coverage requirement for surveillance systems in LTE UL networks. Specifically, we formulate the Camera Set Resource Allocation Problem (CSRAP) and prove that the problem is NP-Hard. We then propose an Integer Linear Programming formulation for general cases to find the optimal solution. Moreover, we present a baseline algorithm and devise an approximation algorithm to solve the problem. Simulation results based on a real surveillance map and synthetic datasets manifest that the number of allocated RBs can be effectively reduced compared to the existing approach for LTE networks.Comment: 9 pages, 10 figure

On Optimal Neighbor Discovery

Mobile devices apply neighbor discovery (ND) protocols to wirelessly initiate a first contact within the shortest possible amount of time and with minimal energy consumption. For this purpose, over the last decade, a vast number of ND protocols have been proposed, which have progressively reduced the relation between the time within which discovery is guaranteed and the energy consumption. In spite of the simplicity of the problem statement, even after more than 10 years of research on this specific topic, new solutions are still proposed even today. Despite the large number of known ND protocols, given an energy budget, what is the best achievable latency still remains unclear. This paper addresses this question and for the first time presents safe and tight, duty-cycle-dependent bounds on the worst-case discovery latency that no ND protocol can beat. Surprisingly, several existing protocols are indeed optimal, which has not been known until now. We conclude that there is no further potential to improve the relation between latency and duty-cycle, but future ND protocols can improve their robustness against beacon collisions.Comment: Conference of the ACM Special Interest Group on Data Communication (ACM SIGCOMM), 201

Minimum Distortion Variance Concatenated Block Codes for Embedded Source Transmission

Some state-of-art multimedia source encoders produce embedded source bit streams that upon the reliable reception of only a fraction of the total bit stream, the decoder is able reconstruct the source up to a basic quality. Reliable reception of later source bits gradually improve the reconstruction quality. Examples include scalable extensions of H.264/AVC and progressive image coders such as JPEG2000. To provide an efficient protection for embedded source bit streams, a concatenated block coding scheme using a minimum mean distortion criterion was considered in the past. Although, the original design was shown to achieve better mean distortion characteristics than previous studies, the proposed coding structure was leading to dramatic quality fluctuations. In this paper, a modification of the original design is first presented and then the second order statistics of the distortion is taken into account in the optimization. More specifically, an extension scheme is proposed using a minimum distortion variance optimization criterion. This robust system design is tested for an image transmission scenario. Numerical results show that the proposed extension achieves significantly lower variance than the original design, while showing similar mean distortion performance using both convolutional codes and low density parity check codes.Comment: 6 pages, 4 figures, In Proc. of International Conference on Computing, Networking and Communications, ICNC 2014, Hawaii, US

Health and safety at work: the prevention model in Italy. WP C.S.D.L.E. “Massimo D’Antona”.IT – 408/2020

A research itinerary aimed at clarifying the substantive content and the type of prevention that shapes the rules for the protection of health and safety of workers in the Italian legal system. The focus will be on the difference between primary and secondary prevention in the warranty of fundamental right