Talk:Hypercomputation/PNDTM

We define a preferential non-deterministic Turing machine as a 7-tuple $$M=(Q, \Sigma, \iota, \sqcup, A, \delta, \leq_A)$$

where


 * $$Q$$ is a finite set of states
 * $$\Sigma$$ is a finite set of symbols (the tape alphabet)
 * $$\iota \in Q$$ is the initial state
 * $$\sqcup$$ is the blank symbol ($$\sqcup \in \Sigma$$)
 * $$A \subseteq Q$$ is the set of accepting states
 * $$\delta: Q \backslash A \times \Sigma \rightarrow \left( Q \times \Sigma \times \{L,R\} \right)$$ is a relation called the "transition function", where L is left shift and R is right shift. \delta associates each combination of a non-accepting state and a tape symbol with one or more succesor states, tape symbols to be written, and L/R movements for the tape head.
 * $$\leq_A: A \times A \rightarrow \{ 0,1 \} $$ is a binary relation which induces a total ordering on A. An accepting state $$a \in A$$ is said to be preferred to state $$b \in A$$ iff $$b \neq a$$ and $$ b \leq_A a$$.