formal.html

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    <h4 class="modal-title"><i>Formal Definition</i></h4>
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        <p>A Turing machine is formally defined (one-tape) as a 7-tuple <b><i>M = ( Q, &Gamma;, b, &sum;, &delta;, q0, F
            )</i></b> where: </p>
        <ul class="list-group">
            <li class="list-group-item"><b>Q</b> is a finite, non-empty set of states</li>
            <li class="list-group-item"><b>&Gamma;</b> is a finite, non-empty set of the tape <i>alphabet/symbols</i>
            </li>
            <li class="list-group-item"><b>b &isin; &Gamma;</b> is the blank symbol (the only symbol allowed to occur on
                the tape infinitely often at any step during the computation)
            </li>
            <li class="list-group-item"><b>&sum; &subseteq; &Gamma; &setminus; {b}</b> is the set of input symbols</li>
            <li class="list-group-item"><b>q0 &in; Q</b> is the initial state</li>
            <li class="list-group-item"><b>F &subseteq; Q</b> is the set of final or accepting states.</li>
            <li class="list-group-item"><b> &delta;: Q &setminus; F &times; &Gamma; &rightarrow;
                Q &times; &Gamma; &times; {L,R}</b> is a partial function called the transition function, where L is
                left shift, R is right shift.
            </li>
        </ul>
        <blockquote>
            <p><i>Anything that operates according to these specifications is a Turing machine.</i></p>
            <footer>Hopcroft and Ullman (1979, p. 148)</footer>
        </blockquote>


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