44,717 research outputs found
Streaming Tree Transducers
Theory of tree transducers provides a foundation for understanding
expressiveness and complexity of analysis problems for specification languages
for transforming hierarchically structured data such as XML documents. We
introduce streaming tree transducers as an analyzable, executable, and
expressive model for transforming unranked ordered trees in a single pass.
Given a linear encoding of the input tree, the transducer makes a single
left-to-right pass through the input, and computes the output in linear time
using a finite-state control, a visibly pushdown stack, and a finite number of
variables that store output chunks that can be combined using the operations of
string-concatenation and tree-insertion. We prove that the expressiveness of
the model coincides with transductions definable using monadic second-order
logic (MSO). Existing models of tree transducers either cannot implement all
MSO-definable transformations, or require regular look ahead that prohibits
single-pass implementation. We show a variety of analysis problems such as
type-checking and checking functional equivalence are solvable for our model.Comment: 40 page
Boundary state analysis on the equivalence of T-duality and Nahm transformation in superstring theory
We investigated the equivalence of the T-duality for a bound state of D2 and
D0-branes with the Nahm transformation of the corresponding gauge theory on a
2-dimensional torus, using the boundary state analysis in superstring theory.
In contrast to the case of a 4-dimensional torus, it changes a sign in a
topological charge, which seems puzzling when regarded as a D-brane charge.
Nevertheless, it is shown that it agrees with the T-duality of the boundary
state, including a minus sign. We reformulated boundary states in the RR-sector
using a new representation of zeromodes, and show that the RR-coupling is
invariant under the T-duality. Finally, the T-duality invariance at the level
of the Chern-Simon coupling is shown by deriving the Buscher rule for the
RR-potentials, known as the 'Hori formula', including the correct sign.Comment: 31 pages. v2: references added, typos correcte
Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction
Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn
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