355 research outputs found

    Repetitive subwords

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    The central notionof thisthesisis repetitionsin words. We studyproblemsrelated to contiguous repetitions. More specifically we will consider repeating scattered subwords of non-primitive words, i.e. words which are complete repetitions of other words. We will present inequalities concerning these occurrences as well as giving apartial solutionto an openproblemposedby Salomaaet al. We will characterize languages, whichare closed under the operation ofduplication, thatis repeating any factor of a word. We alsogive newbounds onthe number of occurrencesof certain types of repetitions of words. We give a solution to an open problem posed by Calbrix and Nivat concerning regular languages consisting of non-primitive words. We alsopresentsomeresultsregarding theduplication closureoflanguages,among which a new proof to a problem of Bovet and Varricchio

    Derivation Languages of Graph Grammars

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    We investigate sequential derivation languages associated with graph grammars, as a loose generalisation of free-labeled Petri nets and Szilard languages. The grammars are used to output strings of rule labels, and the applicability of a special rule determines the acceptance of a preceding derivation.Due to the great power of such grammars, this family of languages is quite large and endowed with many closure properties. All derivation languages are decidable in nondeterministic polynomial time and space O(n log n), by simulation of the graph grammar on a Turing machine

    ‘Genetic Coding’ Reconsidered : An Analysis of Actual Usage

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    I thank George Pandarakalam for research assistance; Hans-Jörg Rheinberger for hosting my stay at the Max Planck Institute for History of Science, Berlin; and Sahotra Sarkar and referees of this journal for offering detailed comments. Funded by the Wellcome Trust (WT098764MA).Peer reviewedPublisher PD

    On lexicographic enumeration of regular and context-free languages

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    We show that it is possible to efficiently enumerate the words of a regular language in lexicographic order. The time needed for generating the next word is O(n) when enumerating words of length n. We also define a class of context-free languages for which efficient enumeration is possible

    Automatic sets of rational numbers

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    The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.Comment: Previous version appeared in Proc. LATA 2012 conferenc

    Bibliographie

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    DEMONIC programming: a computational language for single-particle equilibrium thermodynamics, and its formal semantics

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    Maxwell's Demon, 'a being whose faculties are so sharpened that he can follow every molecule in its course', has been the centre of much debate about its abilities to violate the second law of thermodynamics. Landauer's hypothesis, that the Demon must erase its memory and incur a thermodynamic cost, has become the standard response to Maxwell's dilemma, and its implications for the thermodynamics of computation reach into many areas of quantum and classical computing. It remains, however, still a hypothesis. Debate has often centred around simple toy models of a single particle in a box. Despite their simplicity, the ability of these systems to accurately represent thermodynamics (specifically to satisfy the second law) and whether or not they display Landauer Erasure, has been a matter of ongoing argument. The recent Norton-Ladyman controversy is one such example. In this paper we introduce a programming language to describe these simple thermodynamic processes, and give a formal operational semantics and program logic as a basis for formal reasoning about thermodynamic systems. We formalise the basic single-particle operations as statements in the language, and then show that the second law must be satisfied by any composition of these basic operations. This is done by finding a computational invariant of the system. We show, furthermore, that this invariant requires an erasure cost to exist within the system, equal to kTln2 for a bit of information: Landauer Erasure becomes a theorem of the formal system. The Norton-Ladyman controversy can therefore be resolved in a rigorous fashion, and moreover the formalism we introduce gives a set of reasoning tools for further analysis of Landauer erasure, which are provably consistent with the second law of thermodynamics.Comment: In Proceedings QPL 2015, arXiv:1511.01181. Dominic Horsman published previously as Clare Horsma

    The copying power of one-state tree transducers

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    One-state deterministic top-down tree transducers (or, tree homomorphisms) cannot handle "prime copying," i.e., their class of output (string) languages is not closed under the operation L → {(w(w)f(n) w ε L, f(n) ≥ 1}, where f is any integer function whose range contains numbers with arbitrarily large prime factors (such as a polynomial). The exact amount of nonclosure under these copying operations is established for several classes of input (tree) languages. These results are relevant to the extended definable (or, restricted parallel level) languages, to the syntax-directed translation of context-free languages, and to the tree transducer hierarchy.\ud \u
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