On algorithmic equivalence of instruction sequences for computing bit   string functions
  Every partial function from bit strings of a given length to bit strings of a possibly different 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. We look for an equivalence relation on instruction sequences of this kind that captures to a reasonable degree the intuitive notion that two instruction sequences express the same algorithm. 
J. A. Bergstra, C. A. Middelburg
cs.LO