The Compilation of Reversible Circuits and a New Optimization Game
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The focus of this thesis is reversible circuit compilation. We will explore the use of pebble games for circuit analysis. The usefulness of this technique is demonstrated by finding a new space bound for the Karatsuba algorithm and more generally for any similar algorithm based on recurrence relations. A new pebble game based on the reversible pebble game which better captures the use of in-place operations is also presented. We also construct circuit to compute trigonometric functions based on the CORDIC algorithm and analyze it using this game.