Turing machines, transition systems, and interaction

Some improvements in fuzzy turing machines

In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...

Reactive Turing Machines with Infinite Alphabets

The notion of Reactive Turing machines (RTM) was proposed as an orthogonal extension of Turing machines with interaction. RTMs are used to define the notion of executable transition system in the same way as Turing machines are used to define the notion of computable function on natural numbers. RTMs inherited finiteness of all sets involved from Turing machines, and as a consequence, in a sing...

Symmetries and transitions of bounded Turing machines

We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of the transition monoid at each step. This approach first gives us non-deterministic automata, then (non-deterministic) two-way automata and bounded Turing machines — that is, Turing machines where the read / write head is unable to move pas...

Turing Machines , Transition Systems ,

The Church-Turing Thesis: Breaking the Myth

According to the interactive view of computation, communication happens during the computation, not before or after it. This approach, distinct from concurrency theory and the theory of computation, represents a paradigm shift that changes our understanding of what is computation and how it is modeled. Interaction machines extend Turing machines with interaction to capture the behavior of concu...