In this paper we consider hexagonal arrays on triangular grids and introduce hexagonal local picture languages and hexagonal tiling systems defining hexagonal recognizable picture languages, motivated by an analogous study of rectangular arrays by Giammarresi and Restivo. We also introduce hexagonal Wang tiles to define hexagonal Wang systems (HWS) as a formalism to describe hexagonal picture languages. It is noticed that the family of hexagonal picture languages defined by hexagonal Wang systems and the family recognized by hexagonal tiling systems coincide. Analogous to hv-domino systems describing rectangular arrays, we define xyz-domino systems and prove that recognizable hexagonal picture languages are characterized as projections of xyz-local picture languages.

Two types of Quantum Finite Automata are, the Measure once quantum finite automata (MO-QFA) proposed by Moore and Crutchfield [5] and the Many measure one-way quantum finite automata(MM-QFA) proposed by Kondacs and Waltrous [2]. In both cases it is proved that the language accepted is a subset of regular language. In this paper we define a Quantum Finite Automata using quantum logic. The logic underlying Quantum mechanics is not a Boolean algebra. It is an orthomodular lattice. This logic is called quantum logic By using this logic we study about various properties of QFA's.

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