2013/12/06 by J.A. Bergstra, J. A. Bergstra, Bergstra, J. A. +3 · 3 citations
Computer Science · Mathematics · #Algorithm #Algorithms and Data Compression #Arithmetic #Binary number #Bit (key) #Boolean function #Combinatorics #Computability, Logic, AI Algorithms #Computer hardware #Computer science #Discrete mathematics #F.1.1 #F.2.1 #FOS: Computer and information sciences #Function (biology) #Instruction set #Instructions per cycle #Jump #Mathematics #Multiplication (music) #Parallel computing #Programming Languages (cs.PL) #Programming language #Representation (politics) #Sequence (biology) #Set (abstract data type) #Theoretical computer science #cs.PL #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1312.1812
published in arXiv (Cornell University) (Cornell University) · 17 pages, the preliminaries are about the same as the preliminaries in arXiv:1308.0219 [cs.PL] and arXiv:1312.1529 [cs.PL]; minor errors corrected, references added; section on indirect addressing added
openalex publication_date 2013/12/06 · arxiv created 2014/04/06 · arxiv updated 2014/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. Backward jump instructions are not necessary for this, but instruction sequences can be significantly shorter with them. We take the function on bit strings that models the multiplication of natural numbers on their representation in the binary number system to demonstrate this by means of a concrete example. The example is reason to discuss points concerning the halting problem and the concept of an algorithm.