Abstract We study finite-time bit erasure in the context of majority-logic decoding. In particular, we calculate minimum amount work needed to erase a when one has full control over system dynamics. show that although single unit is easier slow-driving limit, general outperforms fast-erasure limit. Our results also suggest optimal design principles for bits under limited control.

We extend graded modal logic (GML) to a logic that captures the concept of majority. We provide an axiomatization for majority logic, MJL, and sketch soundness and completeness proofs. Along the way, we must answer the question what is a majority of an infinite set? Majority spaces are introduced as a solution to this question.

Rudolph (1967) introduced one-step majority logic decoding for linear codes derived from combinatorial designs. The decoder is easily realizable in hardware and requires that the dual code has to contain blocks of so called geometric designs as codewords. Peterson Weldon (1972) extended Rudolph's algorithm a two-step correcting same number errors Reed's celebrated multi-step decoder. Here, we s...