Abstract
The study proposes our extended method to assess structure complexity for symbol-free sequences, such as literal texts, DNA sequences, rhythm, and musical input. This method is based on L-system and topological entropy for context-free grammar. Inputs are represented as binary trees. Different input features are represented separately within tree structure and actual node contents. Our method infers tree generating grammar and estimates its complexity. This study reviews our previous results on texts and DNA sequences and provides new information regarding them. Also, we show new results measuring complexity of Chinese classical texts and music samples with rhythm and melody components. Our method demonstrates enough sensitivity to extract quasi-regular structured fragments of Chinese texts and to detect irregular styled samples of music inputs. To our knowledge, there is no other method that can detect such quasi-regular patterns.
Highlights
This work introduces general complexity assessment on structure properties for different types of inputs
Input sequences are represented as binary trees, the concept of L-system (Wikipedia 2005) is borrowed to infer rewriting rules and build corresponding contextfree grammars, which are used later to assess the complexity score (Kuich 1970)
Current work is intended to establish a general vision on such kinds of structural complexity assessment
Summary
This work introduces general complexity assessment on structure properties for different types of inputs. Input sequences are represented as binary trees, the concept of L-system (Wikipedia 2005) is borrowed to infer rewriting rules and build corresponding contextfree grammars, which are used later to assess the complexity score (Kuich 1970). This complexity score is closely related to the notion of entropy (Shannon 1948). Our proposed method was applied to the complexity of DNA sequences (Liou et al 2013a, b) From this arose the question of representation: how can other input types be transformed into a binary tree, while keeping the complexity assessment the same? The study turns back to music with an attempt to reconsider the initial assessment, redefine it, and make method capable of naturally incorporating both musical melody and rhythm
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