A uniform approach to test computational complementarity

Studies of computational complementarity properties in finite state interactive automata may shed light on the nature of both quantum and classical computation. But, complementarity is difficult to test even for small-size automata. This paper introduces the concept of an observation graph of an automaton which is used as the main tool for the design of an algorithm which tests, in a uniform manner, two types of complementarity properties. Implementations have been run on a standard desktop computer examining all 5-state binary automata

Computational Complementarity and Sofic Shifts

Finite automata (with outputs but no initial states) have been extensively used as models of computational complementarity, a property which mimics the physical complementarity. All this work was focussed on "frames", i.e., on fixed, static, local descriptions of the system behaviour. In this paper we are mainly interested in the asymptotical description of complementarity.To this aim we will study the asymptotical behaviour of two complementarity principles by associating to every incomplete deterministic automaton (with outputs, but no initial state) certain sofic shifts: automata having the same behaviour correspond to a unique sofic shift. In this way, a class of sofic shifts reflecting complementarity will be introduced and studied. We will prove that there is a strong relation between "local complementarity", as it is perceived at the level of "frames", and "asymptotical complementarity" as it is described by the sofic shift