![]() ![]() ![]() be the squence of configurations of the computation of M. The computation of M in the following way. Simulate a computation of M if M′ can mimic We establish the equivalence of deterministic and nondeterministic Turing machines with an important technique that we call simulation. Remember that we had an algorithm for finite state machines that would convert a nondeterministic finite state machine into a deterministic one that accepted the same language? That algorithm serves as a way to establish the equivalence of dfa's and nfa's. L(M 1 ) = L(M 2 ), we say that C 1 and C 2 are Such that L(M 1 ) = L(M 2 ), we say that C 2 isĪt least as powerful as C 1. Consider two classes of automata C 1and C 2 (suchĪs deterministic finite automata and nondeterministic finite automata). We define equivalence with respect to a machine's ability to accept languages.ĭefinition 10.1 Two automata are equivalent if theyĪccept the same language. In our discussion of the various models of Turing machines we will say that one type of machine is equivalent to another, but what exactly do we mean by equivalence? Equivalence of Classes of Automata 10.1 Minor Variations on the Turing Machine Theme Finally we will discuss a special type of Turing machine called a linear bounded automaton. In this chapter we also discuss nondeterminism in Turing machines and show that, like finite automata but unlike pushdown automata, nondeterminism does not add power to a Turing machine. ![]() In this chapter the author introduces the stay option and shows that it doesn't give a Turing machine any additional power. Your teacher changed his specification from moves being only left or right to moves being left, right, or stay. Actually, in the previous chapter of the book the author does not allow a standard Turing machine the option of having its tape head remain where it is during a transition. Other models have made use of more than one tape, multi-dimensional tapes, and tapes that are infinite in only one direction among other things. In this chapter the author shows that the standard model of Turing machine that we used in the previous chapter is equivalent in power to all the alternative models that theorists have ever proposed. For a plain version of these notes that is more conducive to printing, ![]()
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