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Formal Verification Techniques for Reversible CircuitsLimaye, Chinmay Avinash 27 June 2011 (has links)
As the number of transistors per unit chip area increases, the power dissipation of the chip becomes a bottleneck. New nano-technology materials have been proposed as viable alternatives to CMOS to tackle area and power issues. The power consumption can be minimized by the use of reversible logic instead of conventional combinational circuits. Theoretically, reversible circuits do not consume any power (or consume minimal power) when performing computations. This is achieved by avoiding information loss across the circuit. However, use of reversible circuits to implement digital logic requires development of new Electronic Design Automation techniques. Several approaches have been proposed and each method has its own pros and cons. This often results in multiple designs for the same function. Consequently, this demands research in efficient equivalence checking techniques for reversible circuits.
This thesis explores the optimization and equivalence checking of reversible circuits. Most of the existing synthesis techniques work in two steps — generate an original, often sub-optimal, implementation for the circuit followed optimization of this design. This work proposes the use of Binary Decision Diagrams for optimization of reversible circuits. The proposed technique identifies repeated gate (trivial) as well as non-contiguous redundancies in a reversible circuit. Construction of a BDD for a sub-circuit (obtained by sliding a window of fixed size over the circuit) identifies redundant gates based upon the redundant variables in the BDD. This method was unsuccessful in identifying any additional redundancies in benchmark circuits; however, hidden non-contiguous redundancies were consistently identified for a family of randomly generated reversible circuits. As of now, several research groups focus upon efficient synthesis of reversible circuits. However, little work has been done in identification of redundant gates in existing designs and the proposed peephole optimization method stands among the few known techniques. This method fails to identify redundancies in a few cases indicating the complexity of the problem and the need for further research in this area.
Even for simple logical functions, multiple circuit representations exist which exhibit a large variation in the total number of gates and circuit structure. It may be advantageous to have multiple implementations to provide flexibility in choice of implementation process but it is necessary to validate the functional equivalence of each such design. Equivalence checking for reversible circuits has been researched to some extent and a few pre-processing techniques have been proposed prior to this work. One such technique involves the use of Reversible Miter circuits followed by SAT-solvers to ascertain equivalence. The second half of this work focuses upon the application of the proposed reduction technique to Reversible Miter circuits as a pre-processing step to improve the efficiency of the subsequent SAT-based equivalence checking. / Master of Science
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Investigating the structure and dynamics of DNA with fluorescence and computational techniquesSmith, Darren Andrew January 2015 (has links)
Nucleic acids, such as DNA, play an essential role in all known forms of life; however, despite their fundamental importance, there is still a significant lack of understanding surrounding their functional behaviour. This thesis explores the structure and dynamics of DNA by employing methods based on fluorescence and through the use of computational calculations. Time-resolved fluorescence experiments have been performed on dinucleotides containing 2-aminopurine (2AP) in various alcohol-water mixtures. 2AP, a fluorescent analogue of the nucleobase adenine, has been used extensively to investigate nucleic acids because of its ability to be incorporated into their structures with minimal perturbation and its high sensitivity to its local environment. Direct solvent effects on 2AP were established through measurements on the free fluorophore. Analysis of the complex fluorescence decays associated with the dinucleotides was challenging but has provided insight into their conformational dynamics. Solvent polarity was found to play a significant role in determining both photophysical and conformational properties in these systems. The complicated fluorescence decay of 2AP in nucleic acids highlights the need for accurate and unbiased analysis methods. Various time-resolved fluorescence analysis methods, including iterative reconvolution and the exponential series method, have been investigated with real and simulated data to obtain an overview of their benefits and limitations. The main outcome of the evaluation is that no single method is preferred in all situations and there is likely to be value in using a combination when there is ambiguity in the interpretation of the results. Regardless of the analysis technique used, the parameterised description of the observed fluorescence decay is meaningless if the underlying physical model is unrealistic. The advance of computational methods has provided a new means to rigorously test the viability of proposed models. Calculations have been performed at the M06-2X/6-31+G(d) level of theory to investigate the stability of 2AP-containing dinucleotides in conformations similar to those observed in the double-helical structure of DNA. The results help to explain the similarity of the time-resolved fluorescence behaviour of 2AP in dinucleotide and DNA systems but also bring to light subtle differences that could perhaps account for experimental discrepancies. The recent emergence of advanced optical microscopy techniques has offered the prospect of being able to directly visualise nucleic acid structure at the nanoscale but, unfortunately, limitations of existing labelling methods have hindered delivery of this potential. To address this issue, a novel strategy has been used to introduce reversible fluorescence photoswitching into DNA at high label density. Photophysical studies have implicated aggregation and energy-transfer as possible quenching mechanisms in this system, which could be detrimental to its future application. The reliability of fluorescence photoswitching was investigated at ensemble and single-molecule level and by performing optical lock-in detection imaging. These developments lay the foundations for improved and sequence-specific super-resolution microscopy of DNA, which could offer new insights into the 3D nanoscale structure of this remarkable biopolymer. In summary, the work presented in this thesis outlines important observations and developments that have been made in the study of the structure and dynamics of nucleic acids.
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Les files et les reseaux zero-automatiquesDao Thi, Thu Ha 03 December 2007 (has links) (PDF)
On introduit un nouveau modele de file d'attente: les files Zero-automatiques. Tout d'abord, on considere la discipline de service Premier Arrive Premier Servi. Les files 0-automatiques sont caracterisees par une salle d'attente evoluant suivant un mecanisme de marche aleatoire sur un groupe ou un monoede infini. En considerant les deux cas les plus simples et aussi extremes de files 0-automatiques, nous retrouvons la file simple M/M/1 et la G-file de Gelenbe avec clients positifs et negatifs.<br />Le resultat saillant est que toutes les files 0-automatiques ont une distribution stationnaire a forme produit et un processus de depart de Poisson. C'est un point crucial pour construire les reseaux a forme produit.<br />On considere deux modeles correspondant aux differents routages classiques: reseaux a la Jackson et reseaux a la Kelly. Dans les deux cas, on a montre que la distribution stationnaire est a forme produit et peut etre determinee explicitement. De plus, le processus de depart est Poisson.<br />Enfin, considerons les files 0-automatiques avec discipline de service Dernier Arrive Premier Servi. Dans ce cas, certaines proprietes restent vraies, mais pas toutes. On obtient des resultats interessants en comparant les zones de stabilite d'une meme file 0-automatique sous les discpilines Premier Arrive Premier Servi et Dernier Arrive Premier Servi.
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Regulation of the transcription factor GATA-3 within T cells - Involvement of SIRT1, a class III histone deacetylaseMari, Nathalie 17 October 2008 (has links)
Within the lymphocyte lineage, GATA-3 is a major transcription factor implicated in the regulation of Th1/Th2 differentiation by promoting the expression of the Th2 cytokines, such as IL-4, IL-5, IL-10 and IL-13. Although the role of GATA-3 in the development of the Th2 lineage has been extensively described in the literature, the molecular mechanisms underlying its activity remain to be clarified. Here, we investigated whether GATA-3 might be regulated by reversible acetylation. In vivo, GATA-3 associates with class I and III HDACs. Biochemical studies unraveled the specific association of GATA-3 with the class III member SIRT1. Association with SIRT1 leads to the inhibition of GATA-3-induced IL-5 transcription. Using siRNA, we further show that SIRT1 promotes destabilization of GATA-3. Interestingly, nicotinamide, a specific inhibitor of SIRTs had no effect on the ability of SIRT1 to destabilize GATA-3 and to repress its transcriptional activity. In addition, a catalytic-defective mutant of SIRT1 (H363Y) shows similar effects to wild-type SIRT1, demonstrating that the deacetylase activity of SIRT1 is not required for its regulation of GATA-3. For the first time, our study indicates that SIRT1 is functionally linked to GATA-3. Moreover, our results also suggest that some important SIRT1 functions may not require its deacetylase activity.
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Em busca de um algoritmo construtivo para autômatos celulares reversíveis: a abordagem das regras primitivas e derivadasKronemberger, Guilherme 28 January 2008 (has links)
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Previous issue date: 2008-01-28 / Cellular automata have been studied as computer models in many different areas. They have many properties, one of them being reversibility. Reversible cellular automata can be used, among other applications, for data compressing and encryption. Apparently, the reversible rules featured in the literature seem to have been derived through
exhaustive searches in their corresponding spaces. However, it would be important the availability of an algorithm that would allow their direct and easy construction, different from what occurs in literature. This is the aim of this work. Along this line, we tried to come up with an algorithm to allow the identification of one-dimensional, reversible cellular automaton rules. This was based on reversible rules with 2 states and 2, 3, 4 and 5 cells per neighborhood, and on those with 3 states and 2 and 3 cells per neighborhood, all of them drawn out of exhaustive analysis and from the literature. By studying these rules it was possible to verify in each space that: all reversible rules are balanced; they are symmetrically distributed; a subset of them herein denoted primitive reversible rules, RPs have a simple formation law, defined by homogeneous blocks of states; and, if a rule is reversible, so are all its dynamically equivalent rules. In the attempt to obtain the targetted algorithm, an approach was explored in which the non-primitive reversible rules (the so-called derived rules, RDs) were supposed to be obtained from the primitives. Along this line, two ways to construct the RDs were tried out, one based upon using all RPs jointly as a group, and another, using them individually; however, neither of them led to a positive result. Additionally, relations between the properties of reversibility and conservativity of a rule have also been studied in the rule spaces considered. / Autômatos celulares têm sido estudados como modelos computacionais em diversas áreas, sendo que muitas são as suas propriedades, entre elas a reversibilidade. Autômatos celulares reversíveis podem ser usados, entre outras aplicações, para compactação ou encriptação de dados. Aparentemente, as regras reversíveis apresentadas na literatura parecem ter sido derivadas apenas através de buscas exaustivas em seus espaços correspondentes. No entanto, seria importante a existência de um algoritmo que permitisse construí-las fácil e diretamente, diferente do que acontece na literatura. Este é o objetivo deste trabalho. Neste sentido, buscou-se um algoritmo que permitesse identificar regras de autômatos celulares unidimensionais reversíveis. Para tanto, foram obtidas em análises exaustivas e na literatura todas as regras reversíveis de 2 estados e vizinhanças de 2, 3, 4 e 5 células, e de 3 estados e vizinhanças de 2 e 3 células. Com o estudo destas regras constatou-se em cada espaço que: todas as regras reversíveis são balanceadas; elas se distribuem simetricamente; um subconjunto delas aqui denominadas regras reversíveis primitivas, RPs possui lei de formação simples, definida por blocos homogêneos de estados; e, se uma regra é reversível, todas as suas equivalentes dinâmicas também o são. Na tentativa de se obter o algoritmo desejado explorou-se uma abordagem em que as regras reversíveis não primitivas (denominadas regras derivadas, RDs), seriam obtidas a partir das primitivas. Nesse sentido foram testados dois esquemas de construção das RDs, um baseado na utilização conjunta de todas as RPs, e outro, utilizando-as individualmente; entretanto, ambos não levaram a resultado positivo. Adicionalmente, estudou-se a relação entre as propriedades de reversibilidade e conservatividade de regras nos espaços considerados.
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ON THE DESIGN OF FLUXONICS: REVERSIBLE SUPERCONDUCTING CIRCUITSDewan J Woods (13108551) 18 July 2022 (has links)
<p>In this dissertation, we present work on developing superconducting circuits intended to advance the implementation of Asynchronous Ballistic Reversible Computation using Fluxon Logic. In the first Chapter we introduce the need for developing reversible computing, and discuss implementing asynchronous reversible computing using fluxons in superconducting circuits. In Chapter 2, we introduce basic superconductivity physics, including the Josephson effects, which is necessary to know for understanding the behavior of Josephson junction transmission lines. In Chapter 3, we introduce tools to physically understand the behavior of topologically protected solitons, 'fluxons', in Josephson junction transmission lines. Finally, in Chapter 4, we briefly discuss the history of fluxon-based computation devices and present current state of the art design of such reversible computation devices, including the fluxon Rotary gate that we have developed. Taken together, these represent advances in the direction of implementing asynchronous reversible computing in practice.</p>
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Reversibla 2+1-fält på motortrafikled Utvärdering av restidseffekter för Värmdöpendlare : Utvärdering av restidseffekter för Värmdöpendlare / Reversible 2+1 lanes on motorways : Evaluation of travel time effects for Värmdö commuter.JOHANSSON, JOSEFIN January 2023 (has links)
Värmdö is a commuter municipality to Stockholm. Road 222 between Värmdö and Stockholm is the main commuter route for both bus and car traffic. Road 222 is a bottleneck at Farstabron in the direction towards Värmdö, where the motorway will go from two to one lane and become a non-meeting motorway. Towards Stockholm, the bridge has two lanes, which is why capacity is not affected as strongly in that direction. The accessibility problems arise mainly in the direction of Värmdö during maximum hours in the afternoon and during weekends and summer time as the municipality also has many holiday homes. Measures to improve accessibility have been raised by both the municipality and the Swedish Transport Administration. Building a new bridge is not relevant as the remaining expected technical life of the bridge is long. The Swedish Transport Administration has an idea for a reversible lane solution on the bridge, which is the proposal studied in this thesis. Data collection and traffic analysis has been performed to study how the travel time effect would be if Farstabron was rebuilt into a reversible 2 + 1 road, with or without a reversible bus lane. The tool used is the microsimulation program PTV VISSIM. The results show that a reversible solution without a bus lane is the alternative that provides by far the largest travel time gains for both car and bus in 2040. The degree project contains a chapter that deals with traffic engineering theory and traffic simulation theory as well as a literature study chapter that summarizes the knowledge about reversible lanes. The information about reversible lanes, even international studies, is poor.Experiences of reversible lanes is good and is mainly to be recommended as the flow in one direction is significantly greater than in the other. The traffic safety risk is primarily linked to unprotected road users. The most common internationally according to what has been identified is to implement reversible lanes on motorways with protective barriers. However, no reversible lane without a barrier have been identified holding 80km/h. Studies have shown that reversible lanes could have a cost-benefit ratio of around 7, which means that the benefit outweighed the costs 7 times in money measured. The weaving dynamics of VISSIM from two to one lane were challenging to calibrate against the reality. Preparatory behavior during lane changes is mainly affected by car-following and lane-changing models in VISSIM. In the simulation the correlation with collected data was slightly more accurate with the car following model for W99 (freeway) rather than W74 (weaving urban rd).
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Establishment of in vitro-infection models for Chlamydia trachomatis based on human primary cells and primary tissueZielecki, Julia 10 November 2011 (has links)
Zellkultursysteme mit Krebszelllinien werden seit Langem zur Untersuchung der Interakti-on zwischen Pathogenen und ihren Wirtszellen eingesetzt. Diese Systeme eignen sich aufgrund der reduzierten Komplexität für die Analyse einzelner Faktoren, spiegeln jedoch nicht den Zustand primärer Zellen oder die komplexe Gewebestruktur wieder. Um die Beschränkungen zu umgehen, wurden in dieser Arbeit neue Modelle etabliert auf der Grundlage von reversibel immortalisierten humanen Primärzellen und ex vivo Kultur von intaktem humanem Eileitergewebe. Infektionen mit dem humanpathogenen Bakterium Chlamydia trachomatis, welches chronische Schmerzen oder Unfruchtbarkeit auslösen kann, wurden in diesen Modellen untersucht. Reversible Immortalisierung wurde mit pri-mären human Eileiterzellen (FT Zellen) und humanen Nabelschnurzellen (HUVEC) durchgeführt. Das System basiert auf lentiviralem Gentransfer und dem Cre-lox-System. HUVEC Zellen wurden mit Kombinationen der Onkoproteine hTERT, SV40T und Bmi1 immortalisiert. Immortalisierung von FT Zellen wurde mit SV40T und Bmi1 erreicht. Eine Analyse der FT Zelllinien zeigte Veränderungen des Karyotyps durch die Immortalisie-rung. Bemerkenswerterweise konnten die Stammzellmarker CD44 und Oct4 in FT Zellen nachgewiesen werden. Ex vivo Gewebekultur humaner Eileiter wurde als stabiles Infekti-onsmodel für Chlamydia trachomatis etabliert. Mittels hochauflösender Konfokal-mikroskopie wurde gezeigt, dass die Infektion mit C. trachomatis tiefgreifende Verände-rungen im Epithel der Mukosa auslöst und zum Verlust der Zelladhäsion und Zellpolarität führt. Ein erhöhter Anteil apoptotischer Zellen wurde nach Infektion mit Serovar D beo-bachtet, einem klinischen Isolat des Genitaltraktes. Dieses Ergebnis steht im Gegensatz zu Infektionen mit dem Laborstamm Serovar L2. Phänotypische Veränderungen in nicht infizierten Zellen weisen auf die Existenz parakriner Signalwege während der akuten In-fektion und Veränderung der epithelialen Homeostase hin. / Cell culture systems with cancer-derived cell lines have long been used to study the interaction between pathogens and their host cells. Due to reduced complexity these systems are convenient for the analysis of single factors; however, they do not represent the condition of primary cells or the complex tissue structure. To circumvent these limitations new models were established in this study on the basis of reversibly immortalized human primary cells and ex vivo culture of intact human fallopian tube tissue. Infections with the human pathogenic bacterium Chlamydia trachomatis, which can lead to chronic pain or infertility, were analyzed in these models. Reversible immortalization was applied to primary human fallopian tube (FT) cells and human umbilical vein cells (HUVEC). This system is based on lentiviral gene transfer and the Cre-lox-system. HUVEC cells were immortalized with a combination of two of the oncoproteins hTERT, SV40T and Bmi1. Immortalization of FT cells was achieved with SV40T and Bmi1. Analysis of FT cell lines revealed changes of the karyotype induced by immortalization. Remarkably, the stem cell markers CD44 and Oct4 were detected in FT cells. Ex vivo tissue culture of human fallopian tubes was established as stable and reliable infection model for Chlamydia trachomatis. Via high resolution confocal analysis the infection with C. trachomatis was discovered to trigger profound changes in the epithelial mucosa, causing loss of cell adhesion and polarity. Interestingly, an increase in the rate of apoptotic cells was observed after infection with serovar D, a clinical genital tract isolate. This finding is in contrast to infections with serovar L2, a laboratory strain. Phenotypic changes in non-infected cells suggest the existence of paracrine signalling during acute infection and change in epithelial homeostasis.
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Protein Phosphatase 4 ist ein neuer Regulator der circadianen Uhr in SäugernKlemz, Sabrina 11 September 2014 (has links)
Circadiane Uhren sind endogene Oszillatoren, die tägliche Rhythmen in Physiologie, Metabolismus und Verhalten steuern. Auf molekularem Level wird die Dynamik der circadianen Oszillation über ein genregulatorisches Netzwerk aus transkriptionellen-translationalen Rückkopplungsschleifen gesteuert. Posttranslationale Modifikationen von Uhrproteinen sind für eine präzise Justierung der circadianen Periode essentiell. Dabei spielt die Phosphorylierung von Uhrproteinen für die Regulation von Aktivität, Stabilität und intrazellulärer Lokalisation eine wichtige Rolle. Bisher sind verschiedene Kinasen als Modulatoren der circadianen Uhr charakterisiert worden, jedoch ist eine funktionale Rolle von Protein Phosphatasen bisher nur unzureichend untersucht. In dieser Arbeit wurde mittels eines RNAi-basierten Screenings in oszillierenden humanen Zellen untersucht, ob sich die gezielte Depletion katalytischer Untereinheiten der Serin/Threonin-Phosphatasen auf die normale Oszillationsdynamik auswirkt und welche Rolle ausgewählte Phosphatase-Kandidaten für die posttranslationale Kontrolle des molekularen Oszillators spielen. Die RNAi vermittelte Depletion von Protein Phosphatase 4 führte gewebe- und speziesübergreifend zu einer signifikant kurzen circadianen Periode, während die Überexpression von wildtypischer Pp4c in einer stark reprimierten Amplitude resultierte. Mechanistische Untersuchungen zur funktionellen Relevanz von PP4c für die Regulation der circadianen Uhr zeigten, dass PP4c womöglich eine duale Rolle spielt: Einerseits ist PP4c in die direkte Aktivierung des Bmal1-Promotors über RRE-Elemente involviert. Anderseits wirkt PP4c inhibierend auf die CLOCK/BMAL1-vermittelte, E-Box getriebene Genexpression. Ein favorisiertes Modell fundiert auf der Vermutung, dass eine durch PP4c induzierte Modulation des Phosphorylierungsstatus von BMAL1 zu einem stabilen, aber transktiptionsinaktiven BMAL1 und damit zu einer verstärkten Repression der Uhrgentranskription führt. / Circadian clocks are endogenous oscillators that drive daily rhythms in physiology, metabolism and behavior. On the molecular level the dynamics of circadian oscillations are regulated by a transcriptional-translational gene-regulatory network. Posttranslational modifications of clock proteins are essential for the precise timing of an about 24 hour-period. Among these modifications, protein phosphorylation plays an important role in regulating activity, stability and intracellular localization of clock proteins. Several kinases were characterized as regulators of the circadian clock. However, the function of protein phosphatases, which balance phosphorylation events, in the mammalian clock mechanism is less well understood. By using a systematic RNAi-based approach in oscillating human cells, this work aimed to study the impact of catalytic subunits of Serine/Threonin-phosphatases on normal circadian dynamics and the functional role of potential candidates in the posttranslational control of the mammalian molecular oscillator. This study demonstrates, that genetic depletion of the catalytic subunit of protein phosphatase 4 results independently from tissue and species in a significant shorter period, whereas overexpression of wildtype PP4c results in a severely reduced amplitude rhythm. Mechanistic experiments to uncover the functional relevance of PP4c in the regulation of the circadian clock showed, that PP4c plays a dual role: Firstly, PP4 is involved in the direct activation of the Bmal1-promotor via RRE elements. Secondly, PP4c is inhibiting the CLOCK/BMAL1-mediated gene expression. A favored model is based on the assumption, that PP4c-induced modulation of the phosphorylation status of BMAL1 leads to a more stable and transcriptional inactive protein and thereby to a repression of the transcription of clock genes.
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Explorando a noção de reversibilidade parcial de autômatos celulares elementares em reticulados cíclicosFreitas, Rodrigo da Silva 12 August 2010 (has links)
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Previous issue date: 2010-08-12 / Fundo Mackenzie de Pesquisa / Cellular automata have been studied as computer models in many different forms. Several of its properties have been widely explored, among which reversibility stands out. This property is able to provide a cellular automaton the possibility of having their temporal evolution regenerated backward in time, regardless of its initial configuration, through an inverse cellular automaton. Reversibility is such a well characterized concept that many fundamental results associated with it have been obtained, such as the development of algorithms to enumerate all reversible one-dimensional cellular automata
and the undecidability of this property for cellular automata in dimensions larger than 1. The driving force for the present research is to introduce a new concept involving the reversibility ability of a cellular automaton, the concept of partial reversibility, which is analysed herein according to the pre-images of all initial configurations of a rule, up to a certain length. This new concept may be useful for evolutionary searches for reversible cellular automata, to allow the use of cellular automata in tasks related somehow to the reversibility degree of a rule, or in applications where reversible rules are demonstrably employed, such as in cryptography. To that end, some parameters presumably related to reversibility are studied and compared, and empirical measures (lexicographical and numerical) are addressed. The results involving these empirical measures, showed that is possible to refer to a more partially reversible rule than another, besides revealing properties, apparently unknown so far, involving the pre-images of elementary rules. / Os autômatos celulares têm sido estudados como modelos computacionais de diversas formas. Diversas de suas propriedades têm sido amplamente exploradas, entre elas destacando-se a reversibilidade. Esta propriedade é capaz de fornecer a um autômato celular a possibilidade de ter sua evolução temporal refeita para trás no tempo, independentemente de sua configuração inicial, através de um autômato celular inverso. A reversibilidade é um conceito tão bem caracterizado que muitos resultados fundamentais associados a ela têm sido obtidos, tais como o desenvolvimento de algoritmos para enumerar todos os autômatos celulares unidimensionais reversíveis e a indecidibilidade desta propriedade para autômatos celulares com dimensão maior que 1. A ideia principal deste trabalho é introduzir um novo conceito envolvendo a capacidade de reversibilidade de um autômato celular, o conceito de reversibilidade parcial, que é analisado com base nas pré- imagens de todas configurações iniciais de uma regra, até um determinado tamanho de reticulado. Este novo conceito pode ser útil em buscas evolutivas de autômatos celulares reversíveis, a fim de permitir a utilização de autômatos celulares em tarefas associadas de alguma forma ao grau de reversibilidade de uma regra, ou ainda, em aplicações onde
as regras reversíveis são comprovadamente empregadas, tal como em criptografia. Para tanto, alguns parâmetros supostamente relacionados à reversibilidade são estudados e
comparados, e medidas empíricas (lexicográficas e numéricas) são abordadas. Os resultados obtidos envolvendo essas medidas empíricas mostraram que é possível referir-se a uma regra mais parcialmente reversível do que outra, além de revelar propriedades, até então desconhecidas, envolvendo as pré-imagens das regras elementares.
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