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Optical implementations of mathematical resolution.

R A Schmidt, W T Cathey

|May 11, 2010

Summary

This summary is machine-generated.

This study introduces parallel processing techniques for mathematical resolution using optical logic. It demonstrates a largely parallel formulation for efficient computational reasoning.

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Area of Science:

Computer Science
Artificial Intelligence
Logic

Background:

Mathematical resolution is a key algorithmic technique for automated reasoning.
Current implementations typically use sequential list-processing on electronic computers.
This limits scalability and speed for complex logical problems.

Purpose of the Study:

To present novel data representation and processing techniques for parallelizing mathematical resolution.
To explore the feasibility of implementing resolution using array-based optical logic.
To discuss the parallelization of core resolution operations like unification and search.

Main Methods:

Development of data structures suitable for array-based optical processing.
Adaptation of resolution algorithms (resolvent formation, unification, search) for parallel execution.
Exploration of optical logic principles for computational implementation.

Main Results:

A largely parallel formulation of the mathematical resolution technique is demonstrated.
Techniques are presented for implementing resolution up through the quantified propositional calculus.
The potential for significant speedup using optical technologies is highlighted.

Conclusions:

Parallel processing of mathematical resolution is feasible.
Array-based optical logic offers a promising hardware platform for high-performance resolution systems.
This approach could enhance capabilities in automated reasoning and artificial intelligence.