Implement pattern recognition strategy based on frequency hypothesis

[konard]

Summary

This PR implements a pattern recognition strategy based on the frequency hypothesis proposed in issue #628.

Hypothesis: Everything that has the same frequency of occurrence in multiple contexts is the same thing.

Formula: frequency = total_occurrences_in_all_contexts / total_contexts

Implementation Details

Core Components

1. PatternRecognition.cs - Main algorithm implementation

   • Analyzes patterns across multiple contexts
   • Calculates frequency of occurrence for each pattern
   • Identifies universal patterns (100% frequency)
   • Groups patterns by frequency to find potential equivalences
   • Generates common patterns with placeholders for variable parts

2. PatternRecognitionExperiment.cs - Demonstration experiments

   • Example 1: a a b and a a c → Common pattern: a a *
   • Example 2: a b b and c b b → Common pattern: * b b
   • Additional test cases with longer sequences and multiple contexts
   • Markov chain-like transition patterns

3. PatternRecognitionTest.cs - Comprehensive unit tests

   • Basic pattern analysis
   • Universal pattern detection
   • Common pattern generation
   • Frequency grouping
   • Occurrence counting

Key Features

• Frequency Analysis: Calculates how often each pattern appears across contexts
• Variable Detection: Elements with the same frequency are identified as potential equivalences (variables/placeholders)
• Pattern Extraction: Automatically generates common patterns by replacing variable parts with *
• Scalability: Works with any number of contexts and pattern lengths

Validation

The implementation successfully validates both examples from issue #628:

Example 1

Contexts: a a b, a a c
Result: Common pattern is "a a *"
Analysis: b and c both have frequency 0.5 (appear in 1/2 contexts)
Conclusion: b and c could represent the same variable

Example 2

Contexts: a b b, c b b
Result: Common pattern is "* b b"
Analysis: a and c both have frequency 0.5 (appear in 1/2 contexts)
Conclusion: a and c could represent the same variable

Test Results

All unit tests pass:

• ✓ Basic pattern analysis
• ✓ Universal pattern detection
• ✓ Common pattern generation
• ✓ Frequency grouping
• ✓ Occurrence counting

Related Work

This implementation relates to the Markov chain concept mentioned in the issue comments, where the probability of events depends on frequency of occurrence in different states.

Fixes

Fixes #628

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[konard]

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