355 research outputs found
Repetitive subwords
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
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
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
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
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
DEMONIC programming: a computational language for single-particle equilibrium thermodynamics, and its formal semantics
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
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 → {)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
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