Expressiveness and Extensions of an Instruction Sequence Semigroup (1003.1572v1)

Abstract: PGA, short for ProGram Algebra, describes sequential programs as finite or infinite (repeating) sequences of instructions. The semigroup C of finite instruction sequences was introduced as an equally expressive alternative to PGA. PGA instructions are executed from left to right; most C instructions come in a left-to-right as well as a right-to-left flavor. This thesis builds on C by introducing an alternative semigroup Cg which employs label and goto instructions instead of relative jump instructions as control structures. Cg can be translated to C and vice versa (and is thus equally expressive). It is shown that restricting the instruction sets of C and Cg to contain only finitely many distinct jump, goto or label instructions in either or both directions reduces their expressiveness. Instruction sets with an infinite number of these instructions in both directions (not necessarily all such instructions) do not suffer a loss of expressiveness.