Interference automata

We propose a computing model, the Two-Way Optical Interference Automata (2OIA), that makes use of the phenomenon of optical interference. We introduce this model to investigate the increase in power, in terms of language recognition, of a classical Deter-ministic Finite Automaton (DFA) when endowed with the facility of optical interference.] wherein the classical DFA is augmented with a quantum component of constant size. We test the power of 2OIA against the languages mentioned in the above paper. We give efficient 2OIA algorithms to recognize languages for which 2QCFA machines have been shown to exist, as well as languages whose status visa -vis 2QCFA has been posed as open questions. Finally we show the existence of a language that cannot be recognized by a 2OIA but can be recognized by an O(n 3) space Turing machine. We present a model of automata, the Two-Way Optical Interference Automata (OIA), that uses the phenomenon of interference to recognize languages. We augment the classical 2DFA with an array of sources of monochromatic light and a detector. The guiding principle behind the design of the 2OIA model is to deny it any resource other than a finite control and the ability to create interference. Our interest lies essentially in wave interference; for concreteness and ease of exposition we choose light. Specifically, we address the following question: given a language L ⊆ {a, b} * , an input w ∈ {a, b} * , and a 2DFA augmented with |w| " sources of interference " , is it possible to decide efficiently if w ∈ L by examining their interference patterns? While this question is interesting in its own right, the model abstracts out the phenomenon of interference from quantum automata models [MC00,KW97,BP02,AK03,ANTSV02,AF98] in the most general sense. A typical example of an automata model having a restricted quantum component is the 2-way Finite Automata model with Quantum and Classical states (2QCFA) of Ambainis and Watrous [AW02], which is essentially a classical 2DFA that reads input off a read-only tape and is augmented with a quantum component of constant size: the number of dimensions of the associated Hilbert space does not depend on the input length. Unitary operations on the quantum component, which are performed interleaved ⋆ A preliminary version of this paper appears in the proceedings of the 16th Australasian Workshop on Combinatorial Algorithms (AWOCA 2005).