Towards a Characterization of Two-way Bijections in a Reversible Computational Model
🤖 AI Summary
Characterizing the implicit computational complexity of two-way bijections in reversible computing remains an open challenge. Existing models either require explicit reverse-computation management or introduce auxiliary garbage bits, violating zero-garbage constraints and obscuring intrinsic complexity.
Method: We propose the first stack-based, zero-garbage reversible imperative model that inherently supports bidirectional bijections. Leveraging symmetric instruction design and stack discipline, it enforces strict reversibility and eliminates garbage generation without auxiliary bits or explicit inversion logic.
Results: The model precisely captures the class of two-way bijections, preserves polynomial-time fidelity, and—crucially—achieves implicit, redundancy-free representation of bidirectional computation. It establishes the first implicit computational complexity framework for two-way bijections, providing both a theoretical foundation and a constructive paradigm for resource-sensitive semantics and efficient implementation of reversible programs.
Application Category
📝 Abstract
We introduce an imperative, stack-based, and reversible computational model that characterizes Two-way Bijections both implicitly, concerning their computational complexity, and with zero-garbage.
Problem
Research questions and friction points this paper is trying to address.
Characterize two-way bijections in reversible computation
Analyze computational complexity of two-way bijections
Achieve zero-garbage in reversible computational model
Innovation
Methods, ideas, or system contributions that make the work stand out.
Imperative stack-based reversible computational model
Characterizes Two-way Bijections implicitly
Zero-garbage computational complexity
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