Optimizing Reversible Simulation of Injective Functions

Bennett showed that a clean reversible simulation of injective programs is possible without returning the input of a program as additional output. His method involves two computation and two uncomputation phases. This paper proposes an optimization of Bennett's simulation that requires only half of the computation and uncomputation steps for a class of injective programs. A practical consequence is that the reversible simulation runs twice as fast as Bennett's simulation. The proposed method is demonstrated by developing lossless encoders and decoders for run-length encoding and range coding. The range-coding program is further optimized by conserving the model over the text-generation phase. This paper may thus provide a new view on developing efficient reversible simulations for a certain class of injective functions.