Implement an event-driven state machine algorithm in JavaScript for a budgeting tool using React Native and Firebase. Provide:
- Problem definition with input/output and performance requirements
- Algorithm design with complexity analysis
- Core implementation with type annotations and error handling
- At least 2 optimizations with trade-offs and benchmarking
- Complete test suite including unit, edge case, and performance tests
- 3 usage examples and integration pattern
- Documentation with complexity table and decision guide

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