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Computable symbolic dynamics

Mathematical Logic Quarterly, 2008
AbstractWe investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2ℕ to 2ℕ such that P is the set of itineraries of elements of 2ℕ.
Douglas Cenzer
exaly   +3 more sources

A review of symbolic dynamics and symbolic reconstruction of dynamical systems

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023
Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of ...
Yoshito Hirata, José M. Amigó
openaire   +2 more sources

Symbolic Fractional Dynamics

IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2013
Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as ...
Machado, J. A. Tenreiro   +1 more
openaire   +2 more sources

Dressed symbolic dynamics

Physical Review E, 2003
A strange attractor (SA) with symmetry group G can be mapped down to an image strange attractor SA without symmetry by a smooth mapping with singularities. The image SA can be lifted to many distinct structurally stable strange attractors, each equivariant under G, all with the same image SA.
Robert, Gilmore, Christophe, Letellier
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Augmented dynamic symbolic execution

Proceedings of the 27th IEEE/ACM International Conference on Automated Software Engineering, 2012
Dynamic symbolic execution (DSE) can efficiently explore all simple paths through a program, reliably determining whether there are any program crashes or violations of assertions or code contracts. However, if such automated oracles do not exist, the traditional approach is to present the developer a small and representative set of tests in order to ...
Konrad Jamrozik   +3 more
openaire   +1 more source

Symbols and dynamics in the brain

Biosystems, 2001
The work of physicist and theoretical biologist Howard Pattee has focused on the roles that symbols and dynamics play in biological systems. Symbols, as discrete functional switching-states, are seen at the heart of all biological systems in the form of genetic codes, and at the core of all neural systems in the form of informational mechanisms that ...
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On g-measures in symbolic dynamics

Israel Journal of Mathematics, 2010
In the theory of finite-valued stationary processes the class of Markov chains plays a fundamental role. In particular, the topological supports of finite \(n\)-step Markov chains form the class of shifts of finite type that are of first importance in symbolic dynamics. One of the natural generalizations of Markov chains is the class of finitary Markov
Krieger, Wolfgang, Weiss, Benjamin
openaire   +1 more source

Dynamic symbolic execution for polymorphism

Proceedings of the 26th International Conference on Compiler Construction, 2017
Symbolic execution is an important program analysis technique that provides auxiliary execution semantics to execute programs with symbolic rather than concrete values. There has been much recent interest in symbolic execution for automatic test case generation and security vulnerability detection, resulting in various tools being deployed in academia ...
Li, Lian, Lu, Yi, Xue, Jingling
openaire   +3 more sources

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