22 research outputs found

    DNA Computing: Modelling in Formal Languages and Combinatorics on Words, and Complexity Estimation

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    DNA computing, an essential area of unconventional computing research, encodes problems using DNA molecules and solves them using biological processes. This thesis contributes to the theoretical research in DNA computing by modelling biological processes as computations and by studying formal language and combinatorics on words concepts motivated by DNA processes. It also contributes to the experimental research in DNA computing by a scaling comparison between DNA computing and other models of computation. First, for theoretical DNA computing research, we propose a new word operation inspired by a DNA wet lab protocol called cross-pairing polymerase chain reaction (XPCR). We define and study a word operation called word blending that models and generalizes an unexpected outcome of XPCR. The input words are uwx and ywv that share a non-empty overlap w, and the output is the word uwv. Closure properties of the Chomsky families of languages under this operation and its iterated version, the existence of a solution to equations involving this operation, and its state complexity are studied. To follow the XPCR experimental requirement closely, a new word operation called conjugate word blending is defined, where the subwords x and y are required to be identical. Closure properties of the Chomsky families of languages under this operation and the XPCR experiments that motivate and implement it are presented. Second, we generalize the sequence of Fibonacci words inspired by biological concepts on DNA. The sequence of Fibonacci words is an infinite sequence of words obtained from two initial letters f(1) = a and f(2)= b, by the recursive definition f(n+2) = f(n+1)*f(n), for all positive integers n, where * denotes word concatenation. After we propose a unified terminology for different types of Fibonacci words and corresponding results in the extensive literature on the topic, we define and explore involutive Fibonacci words motivated by ideas stemming from theoretical studies of DNA computing. The relationship between different involutive Fibonacci words and their borderedness and primitivity are studied. Third, we analyze the practicability of DNA computing experiments since DNA computing and other unconventional computing methods that solve computationally challenging problems often have the limitation that the space of potential solutions grows exponentially with their sizes. For such problems, DNA computing algorithms may achieve a linear time complexity with an exponential space complexity as a trade-off. Using the subset sum problem as the benchmark problem, we present a scaling comparison of the DNA computing (DNA-C) approach with the network biocomputing (NB-C) and the electronic computing (E-C) approaches, where the volume, computing time, and energy required, relative to the input size, are compared. Our analysis shows that E-C uses a tiny volume compared to that required by DNA-C and NB-C, at the cost of the E-C computing time being outperformed first by DNA-C and then by NB-C. In addition, NB-C appears to be more energy efficient than DNA-C for some input sets, and E-C is always an order of magnitude less energy efficient than DNA-C

    Los presupuestos fácticos de la prevención general. Una aproximación empírica al rol de la disuasión en la enunciación de la Ley penal

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    Programa de Doctorado en Criminología por la Universidad de Granada; la Universidad de Murcia y la Universidad Miguel Hernández de ElcheUna de las justificaciones más comunes sobre la pena es que la misma sirve para prevenir delitos y lo haría desde su misma fase de enunciación que consistiría en la comunicación de una amenaza legal. Esta asunción está tan interiorizada en la sociedad y en el legislador que una forma habitual de justificar la criminalización de nuevas conductas y aumentar las penas es apelar a la necesidad de aumentar los costes del delito para que los potenciales infractores se retraigan de cometer delitos, algo que supuestamente sucedería si se modifica el Código Penal en tal sentido. Sin embargo, se ha tendido a aceptar que la pena cumpliría tal función sin preocuparse ni el legislador ni la dogmática de atender a la multitud de estudios procedentes de las ciencias sociales que ayudarían a determinar qué mecanismos están detrás de la prevención que puede producir la enunciación del castigo. En el presente trabajo se ha tenido, por tanto, un doble objetivo de investigación: por un lado, poner a prueba la hipótesis que se encuentra detrás de la estrategia legislativa consistente en aumentar las penas y los ámbitos de criminalización esperando que ello produzca en los potenciales infractores una necesidad de retraerse de realizar determinadas conductas; y, por otro, poner de manifiesto otra serie de factores que pueden estar relacionados con la prevención producida por la enunciación de la norma penal y que van más allá de la mera intimidación, relacionados con la comunicación del modelo de conducta social y la legitimidad sustantiva de las normas. La consecución de ambos objetivos se ha llevado a cabo por dos vías: por un lado, mediante una revisión bibliográfica de la literatura sobre la teoría de la disuasión general y de otros factores relacionados con el cumplimiento como son la influencia social y la legitimidad sustantiva de la norma; por otro, con la realización de seis estudios empíricos propios en los que se han puesto a prueba las diferentes hipótesis de los principales enfoques de cumplimiento normativo. Entre los principales resultados se encuentran que las variables de la disuasión no suelen formar parte de los elementos que los sujetos de las muestras toman en consideración para la decisión de cumplir. Este hallazgo iría en la línea de lo establecido en la literatura sobre la disuasión que viene a sostener que para que la misma pueda desplegar sus efectos deben de darse toda una serie de requisitos que, normalmente, no se cumplen. En cambio, sí tienen mucha más importancia para dicho cumplimiento variables relacionadas con la transmisión del modelo de conducta normativo, la desaprobación moral social, o el juicio moral o sistema de valores del individuo. En este mismo sentido, una ausencia de cualidades de la norma como la legitimidad percibida de la misma puede producir efectos perversos que derivarían en el incumplimiento y la erosión de la legitimidad de la norma y la autoridad, confirmando la necesidad de que la norma penal revista de legitimidad para que la misma genere cumplimiento voluntario. Finalmente, se establecen algunas conclusiones para la criminología, el Derecho penal y la política criminal derivadas de la investigación y que contribuirían a mejorar, por un lado, el debate sobre los efectos de la sanción penal y, por otro, la parte de la política criminal que corresponde a la regulación y sanción de determinadas conductas socialmente disvaliosas

    On some one-sided dynamics of cellular automata

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    A dynamical system consists of a space of all possible world states and a transformation of said space. Cellular automata are dynamical systems where the space is a set of one- or two-way infinite symbol sequences and the transformation is defined by a homogenous local rule. In the setting of cellular automata, the geometry of the underlying space allows one to define one-sided variants of some dynamical properties; this thesis considers some such one-sided dynamics of cellular automata. One main topic are the dynamical concepts of expansivity and that of pseudo-orbit tracing property. Expansivity is a strong form of sensitivity to the initial conditions while pseudo-orbit tracing property is a type of approximability. For cellular automata we define one-sided variants of both of these concepts. We give some examples of cellular automata with these properties and prove, for example, that right-expansive cellular automata are chain-mixing. We also show that left-sided pseudo-orbit tracing property together with right-sided expansivity imply that a cellular automaton has the pseudo-orbit tracing property. Another main topic is conjugacy. Two dynamical systems are conjugate if, in a dynamical sense, they are the same system. We show that for one-sided cellular automata conjugacy is undecidable. In fact the result is stronger and shows that the relations of being a factor or a susbsystem are undecidable, too

    Cellular automata with complicated dynamics

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    A subshift is a collection of bi-infinite sequences (configurations) of symbols where some finite patterns of symbols are forbidden to occur. A cellular automaton is a transformation that changes each configuration of a subshift into another one by using a finite look-up table that tells how any symbol occurring at any possible context is to be changed. A cellular automaton can be applied repeatedly on the configurations of the subshift, thus making it a dynamical system. This thesis focuses on cellular automata with complex dynamical behavior, with some different definitions of the word “complex”. First we consider a naturally occurring class of cellular automata that we call multiplication automata and we present a case study with the point of view of symbolic, topological and measurable dynamics. We also present an application of these automata to a generalized version of Mahler’s problem. For different notions of complex behavior one may also ask whether a given subshift or class of subshifts has a cellular automaton that presents this behavior. We show that in the class of full shifts the Lyapunov exponents of a given reversible cellular automaton are uncomputable. This means that in the dynamics of reversible cellular automata the long term maximal propagation speed of a perturbation made in an initial configuration cannot be determined in general from short term observations. In the last part we construct, on all mixing sofic shifts, diffusive glider cellular automata that can decompose any finite configuration into two distinct components that shift into opposing direction under repeated action of the automaton. This implies that every mixing sofic shift has a reversible cellular automaton all of whose directions are sensitive in the sense of the definition of Sablik. We contrast this by presenting a family of synchronizing subshifts on which all reversible cellular automata always have a nonsensitive direction

    Theoretical and Practical Aspects Related to the Avoidability of Patterns in Words

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    This thesis concerns repetitive structures in words. More precisely, it contributes to studying appearance and absence of such repetitions in words. In the first and major part of this thesis, we study avoidability of unary patterns with permutations. The second part of this thesis deals with modeling and solving several avoidability problems as constraint satisfaction problems, using the framework of MiniZinc. Solving avoidability problems like the one mentioned in the past paragraph required, the construction, via a computer program, of a very long word that does not contain any word that matches a given pattern. This gave us the idea of using SAT solvers. Representing the problem-based SAT solvers seemed to be a standardised, and usually very optimised approach to formulate and solve the well-known avoidability problems like avoidability of formulas with reversal and avoidability of patterns in the abelian sense too. The final part is concerned with a variation on a classical avoidance problem from combinatorics on words. Considering the concatenation of i different factors of the word w, pexp_i(w) is the supremum of powers that can be constructed by concatenation of such factors, and RTi(k) is then the infimum of pexp_i(w). Again, by checking infinite ternary words that satisfy some properties, we calculate the value RT_i(3) for even and odd values of i

    Unary patterns under permutations

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    Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, and other questions of recent interest. Unary patterns with permutations have been previously analysed only for lengths up to 3. Consider a pattern p=πi1(x)πir(x)p=\pi_{i_1}(x)\ldots \pi_{i_r}(x), with r4r\geq 4, xx a word variable over an alphabet Σ\Sigma and πij\pi_{i_j} function variables, to be replaced by morphic or antimorphic permutations of Σ\Sigma. If Σ3|\Sigma|\ge 3, we show the existence of an infinite word avoiding all pattern instances having x2|x|\geq 2. If Σ=3|\Sigma|=3 and all πij\pi_{i_j} are powers of a single morphic or antimorphic π\pi, the length restriction is removed. For the case when π\pi is morphic, the length dependency can be removed also for Σ=4|\Sigma|=4, but not for Σ=5|\Sigma|=5, as the pattern xπ2(x)π56(x)π33(x)x\pi^2(x)\pi^{56}(x)\pi^{33}(x) becomes unavoidable. Thus, in general, the restriction on xx cannot be removed, even for powers of morphic permutations. Moreover, we show that for every positive integer nn there exists NN and a pattern πi1(x)πin(x)\pi^{i_1}(x)\ldots \pi^{i_n}(x) which is unavoidable over all alphabets Σ\Sigma with at least NN letters and π\pi morphic or antimorphic permutation

    Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type

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    Subshifts are sets of configurations over an infinite grid defined by a set of forbidden patterns. In this thesis, we study two-dimensional subshifts offinite type (2D SFTs), where the underlying grid is Z2 and the set of for-bidden patterns is finite. We are mainly interested in the interplay between the computational power of 2D SFTs and their geometry, examined through the concept of expansive subdynamics. 2D SFTs with expansive directions form an interesting and natural class of subshifts that lie between dimensions 1 and 2. An SFT that has only one non-expansive direction is called extremely expansive. We prove that in many aspects, extremely expansive 2D SFTs display the totality of behaviours of general 2D SFTs. For example, we construct an aperiodic extremely expansive 2D SFT and we prove that the emptiness problem is undecidable even when restricted to the class of extremely expansive 2D SFTs. We also prove that every Medvedev class contains an extremely expansive 2D SFT and we provide a characterization of the sets of directions that can be the set of non-expansive directions of a 2D SFT. Finally, we prove that for every computable sequence of 2D SFTs with an expansive direction, there exists a universal object that simulates all of the elements of the sequence. We use the so called hierarchical, self-simulating or fixed-point method for constructing 2D SFTs which has been previously used by Ga´cs, Durand, Romashchenko and Shen.Siirretty Doriast

    On the aperiodic avoidability of binary patterns with variables and reversals

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    In this work we present a characterisation of the avoidability of all unary and binary patterns, that do not only contain variables but also reversals of their instances, with respect to aperiodic infinite words. These types of patterns were studied recently in either more general or particular cases
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