Prescribed Teams of Rules Working on Several Objects

Abstract

In this paper we consider prescribed sets of rules working on several objects either in parallel – in this case the rules have to take different objects – or else sequentially in any order – in this case several rules may take the same object to work on. We show that prescribed teams of size two, i.e., containing exactly two rules, are sufficient to obtain computational completeness for strings with the simple rules being of the form aIR(b) – meaning that a symbol b can be inserted on the right-hand side of a string ending with a – and DR(b) meaning that a symbol b is erased on the right-hand side of a string. This result is established for systems starting with three initial strings. Using prescribed teams of size three, we may start with only two strings, ending up with the output string and the second string having been reduced to the empty string. We also establish similar results when using the generation of the anti-object b− on the right-hand side of a string instead of deleting the object b, i.e. bIR(b−) inserts the anti object b− and the annihilation rule b b− assumed to happen immediately whenever b and b− meet deletes the b.