An Instruction Sequence Semigroup with Involutive Anti-Automorphisms

Abstract

We introduce an algebra of instruction sequences by presenting a semigroup C in which programs can be represented without directional bias: in terms of the next instruction to be executed, C has both forward and backward instructions and a C-expression can be interpreted starting from any instruction. We provide equations for thread extraction, i.e., C's program semantics. Then we consider thread extraction compatible (anti-)homomorphisms and (anti-)automorphisms. Finally we discuss some expressiveness results.