<h1 id="another-example-title">
<span class="section_number">
{{ chapter.number }}.
</span>
Another Example Title
</h1>
<div>
<img class="" src="{% static 'totally-legit-image.png' %}"/>
</div>
<p>This is a sentence.</p>
<p>Here's another FSA to consider:</p>
<div>
<img alt="FSA with missing transitions" class="" src="{% static 'finite-state-automata-no-trap-example.png' %}"/>
</div>
<p>It's fairly clear what it will accept: strings like "ab", "abab", "abababababab", and, of course {math}\epsilon{math end}.
But there are some missing transitions: if you are in state 1 and get a "b" there's nowhere to go.
If an input cannot be accepted, it will be rejected, as in this case. We could have put in a trap state to make this clear:</p>
<div>
<img alt="FSA with missing transitions" class="" src="{% static 'finite-state-automata-trap-added-example.png' %}"/>
</div>
<p>But things can get out of hand. What if there are more letters in the alphabet? We'd need something like this:</p>
<div>
<img alt="FSA with missing transitions" class="" src="{% static 'finite-state-automata-trap-added-extreme-example.png' %}"/>
</div>
<p>So, instead, we just say that any unspecified transition causes the input to be rejected (that is, it behaves as though it goes into a trap state). In other words, it's fine to use the simple version above, with just two transitions.</p>
<p><a class="glossary-term" data-glossary-term="hello"></a></p>
<p>The most precise way of giving a set of instructions is in the form of a <a class="glossary-term" data-glossary-term="algorithm" id="glossary-algorithm">program</a>,
which is a specific implementation of an algorithm, written in a specific programming language, with a very specific result for any particular input.</p>
<p>Because algorithms exist even if they aren't turned in to programs, we won't need to look at programs at all for this topic, unless you particularly want to.</p>
<p><a class="glossary-term" data-glossary-term="algorithm" id="glossary-algorithm-2"></a></p>
<p>They also happen to be great for illustrating some of the key concepts that arise with algorithms.</p>
<p><a class="glossary-term" data-glossary-term="algorithm" id="glossary-algorithm-3"></a></p>
<p><a class="glossary-term" data-glossary-term="algorithm" id="glossary-algorithm-4"></a></p>
