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Mathematical Properties Of Linguistic Theories: Decidability, Capacity, And Recognition Complexity.pdf

P83-1015.pdf
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🔗 Source: aclanthology.org
📊 Size: 823 KB
👤 Author: C. Raymond Perrault
⬇️ Downloads: 26

Summary

The theories covered include:

1. Context-Free Grammars (CFGs): These have been extensively studied since Chomsky and Miller's early work, with numerous published results on their theoretical properties.

2. Transformational Grammars: Results exist regarding their theory, though less attention has been devoted to discussing their significance compared to other formalisms.

3. Lexical Functional Grammars (LFGs): The document mentions brief comments in the literature about related empirical issues but avoids comparing one theory's adequacy over another.

4. Generalized Phrase Structure Grammars (GPSGs): Studies have been undertaken, such as Warren [51] and Montague's PTQ [30].

5. Tree Adjunct Grammars: Although not examined in detail here, they are part of the broader survey.

The paper delves into complexity theory concepts to discuss computational resources required by algorithms for recognizing these languages. It introduces terms like regular languages, context-tree (CT) languages, context-sensitive (CS) languages, recursive languages, and recursively enumerable (r.e.) languages. The discussion extends to sequential and parallel models of computation, highlighting how syntactic models' complexity is affected by changes in machine architecture.

Furthermore, it covers the concept of worst-case time complexity (O-notation), where functions are classified based on their growth rates as input size increases. The survey also touches upon the transition from sequential to parallel algorithms and their impact on problem difficulty.

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Description

Despite significant work on formalisms, less emphasis has been placed on interpreting these mathematical properties in the context of linguistic theory.

Technical Information

  • File Format: PDF
  • File Size: 823 KB
  • Pages: 8
  • Language: EN
  • Author: C. Raymond Perrault
  • Total Downloads: 26
  • Last Updated: 7 days ago

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