Turing machines based on unsharp quantum logic

Turing machines based on unsharp quantum logic

In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E , we introduce E -valued non-deterministic Turing machines (E NTMs) and E -valued deterministic Turing machines (E DTMs). We discuss different E valued recursively enumerable languages from width-first and depth-first recognition. We find that width-first recog...

Automata theory based on unsharp quantum logic

By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and on...

Quantum Logic, Quantum Histories and Quantum Turing Machines

Some relations between quantum Turing machines and Turing machines

For quantum Turing machines we present three elements: Its components, its time evolution operator and its local transition function. The components are related with the components of deterministic Turing machines, the time evolution operator is related with the evolution of reversible Turing machines and the local transition function is related with the transition function of probabilistic and...

On the simulation of quantum turing machines

In this article we shall review several basic de-nitions and results regarding quantum computation. In particular, after de-ning Quantum Turing Machines and networks the paper contains an exposition on continued fractions and on errors in quantum networks. The topic of simulation of Quantum Turing Machines by means of obvious computation is introduced. We give a full discussion of the simulatio...