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POWhat is the algorithm for generating a random Deterministic Finite Automata?
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2011-04-02T20:24:43.723
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2015-04-24T14:20:53.957
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2011-04-02T20:49:31.717
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Body
The DFA must have the following four properties: <ul> <li>The DFA has N nodes</li> <li>Each node has 2 outgoing transitions.</li> <li>Each node is reachable from every other node.</li> <li>The DFA is chosen with perfectly uniform randomness from all possibilities</li> </ul> This is what I have so far: <ol> <li>Start with a collection of N nodes.</li> <li>Choose a node that has not already been chosen.</li> <li>Connect its output to 2 other randomly selected nodes</li> <li>Label one transition 1 and the other transition 0.</li> <li>Go to 2, unless all nodes have been chosen.</li> <li>Determine if there is a node with no incoming connections.</li> <li>If so, steal an incoming connection from a node with more than 1 incoming connection.</li> <li>Go to 6, unless there are no nodes with no incoming connections</li> </ol> However, this is algorithm is not correct. Consider the graph where node 1 has its two connections going to node 2 (and vice versa), while node 3 has its two connection going to node 4 (and vice versa). That is something like: 1 <==> 2 3 <==> 4 Where, by <==> I mean two outgoing connections both ways (so a total of 4 connections). This seems to form 2 cliques, which means that not every state is reachable from every other state. Does anyone know how to complete the algorithm? Or, does anyone know another algorithm? I seem to vaguely recall that a binary tree can be used to construct this, but I am not sure about that.
Tags
<algorithm><random><finite-automata><dfa><finite-state-machine>
Title
What is the algorithm for generating a random Deterministic Finite Automata?
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