diff --git a/lucene/CHANGES.txt b/lucene/CHANGES.txt
index ed227f8bfae..0b2509bb623 100644
--- a/lucene/CHANGES.txt
+++ b/lucene/CHANGES.txt
@@ -123,6 +123,9 @@ New Features
   attributes package that can be used for TokenStreams that solely produce
   binary terms.  (Uwe Schindler)
 
+* LUCENE-6365: Add Operations.topoSort, to run topological sort of the
+  states in an Automaton (Markus Heiden via Mike McCandless)
+
 API Changes
 
 * LUCENE-6508: Simplify Lock api, there is now just 
diff --git a/lucene/core/src/java/org/apache/lucene/util/automaton/Operations.java b/lucene/core/src/java/org/apache/lucene/util/automaton/Operations.java
index d57184606d2..c0096769e0d 100644
--- a/lucene/core/src/java/org/apache/lucene/util/automaton/Operations.java
+++ b/lucene/core/src/java/org/apache/lucene/util/automaton/Operations.java
@@ -1420,4 +1420,33 @@ final public class Operations {
     result.finishState();
     return result;
   }
+
+  /** Returns the topological sort of all states.  Behavior is undefined if this
+   *  automaton has cycles.  CPU cost is O(numTransitions). */
+  public static int[] topoSortStates(Automaton a) {
+    int numStates = a.getNumStates();
+    int[] states = new int[numStates];
+    final BitSet visited = new BitSet(numStates);
+    final LinkedList<Integer> worklist = new LinkedList<>();
+    worklist.add(0);
+    visited.set(0);
+    int upto = 0;
+    states[upto] = 0;
+    upto++;
+    Transition t = new Transition();
+    while (worklist.size() > 0) {
+      int s = worklist.removeFirst();
+      int count = a.initTransition(s, t);
+      for (int i=0;i<count;i++) {
+        a.getNextTransition(t);
+        if (!visited.get(t.dest)) {
+          visited.set(t.dest);
+          worklist.add(t.dest);
+          states[upto++] = t.dest;
+        }
+      }
+    }
+
+    return states;
+  }
 }
diff --git a/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java b/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java
index 8919acfaa73..7e31e6cd771 100644
--- a/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java
+++ b/lucene/suggest/src/java/org/apache/lucene/search/suggest/analyzing/AnalyzingSuggester.java
@@ -23,12 +23,10 @@ import java.io.IOException;
 import java.nio.file.Files;
 import java.nio.file.Path;
 import java.util.ArrayList;
-import java.util.BitSet;
 import java.util.Collection;
 import java.util.Collections;
 import java.util.Comparator;
 import java.util.HashSet;
-import java.util.LinkedList;
 import java.util.List;
 import java.util.Set;
 
@@ -272,33 +270,6 @@ public class AnalyzingSuggester extends Lookup implements Accountable {
     }
   }
 
-  private int[] topoSortStates(Automaton a) {
-    int numStates = a.getNumStates();
-    int[] states = new int[numStates];
-    final BitSet visited = new BitSet(numStates);
-    final LinkedList<Integer> worklist = new LinkedList<>();
-    worklist.add(0);
-    visited.set(0);
-    int upto = 0;
-    states[upto] = 0;
-    upto++;
-    Transition t = new Transition();
-    while (worklist.size() > 0) {
-      int s = worklist.removeFirst();
-      int count = a.initTransition(s, t);
-      for (int i=0;i<count;i++) {
-        a.getNextTransition(t);
-        if (!visited.get(t.dest)) {
-          visited.set(t.dest);
-          worklist.add(t.dest);
-          states[upto++] = t.dest;
-        }
-      }
-    }
-    return states;
-  }
-
-
   // Replaces SEP with epsilon or remaps them if
   // we were asked to preserve them:
   private Automaton replaceSep(Automaton a) {
@@ -311,7 +282,7 @@ public class AnalyzingSuggester extends Lookup implements Accountable {
     // Go in reverse topo sort so we know we only have to
     // make one pass:
     Transition t = new Transition();
-    int[] topoSortStates = topoSortStates(a);
+    int[] topoSortStates = Operations.topoSortStates(a);
     for(int i=0;i<topoSortStates.length;i++) {
       int state = topoSortStates[topoSortStates.length-1-i];
       int count = a.initTransition(state, t);
diff --git a/lucene/suggest/src/java/org/apache/lucene/search/suggest/document/CompletionTokenStream.java b/lucene/suggest/src/java/org/apache/lucene/search/suggest/document/CompletionTokenStream.java
index 483cfa288c4..38728812271 100644
--- a/lucene/suggest/src/java/org/apache/lucene/search/suggest/document/CompletionTokenStream.java
+++ b/lucene/suggest/src/java/org/apache/lucene/search/suggest/document/CompletionTokenStream.java
@@ -18,9 +18,7 @@ package org.apache.lucene.search.suggest.document;
  */
 
 import java.io.IOException;
-import java.util.BitSet;
 import java.util.Iterator;
-import java.util.LinkedList;
 import java.util.Set;
 
 import org.apache.lucene.analysis.TokenStream;
@@ -245,7 +243,7 @@ public final class CompletionTokenStream extends TokenStream {
     // Go in reverse topo sort so we know we only have to
     // make one pass:
     Transition t = new Transition();
-    int[] topoSortStates = topoSortStates(a);
+    int[] topoSortStates = Operations.topoSortStates(a);
     for (int i = 0; i < topoSortStates.length; i++) {
       int state = topoSortStates[topoSortStates.length - 1 - i];
       int count = a.initTransition(state, t);
@@ -281,32 +279,6 @@ public final class CompletionTokenStream extends TokenStream {
     return result;
   }
 
-  private static int[] topoSortStates(Automaton a) {
-    int numStates = a.getNumStates();
-    int[] states = new int[numStates];
-    final BitSet visited = new BitSet(numStates);
-    final LinkedList<Integer> worklist = new LinkedList<>();
-    worklist.add(0);
-    visited.set(0);
-    int upto = 0;
-    states[upto] = 0;
-    upto++;
-    Transition t = new Transition();
-    while (worklist.size() > 0) {
-      int s = worklist.removeFirst();
-      int count = a.initTransition(s, t);
-      for (int i=0;i<count;i++) {
-        a.getNextTransition(t);
-        if (!visited.get(t.dest)) {
-          visited.set(t.dest);
-          worklist.add(t.dest);
-          states[upto++] = t.dest;
-        }
-      }
-    }
-    return states;
-  }
-
   /**
    * Attribute providing access to the term builder and UTF-16 conversion
    */