diff --git a/runtime/Java/src/org/antlr/v4/runtime/dfa/DFA.java b/runtime/Java/src/org/antlr/v4/runtime/dfa/DFA.java
index 195565646..2da700af4 100644
--- a/runtime/Java/src/org/antlr/v4/runtime/dfa/DFA.java
+++ b/runtime/Java/src/org/antlr/v4/runtime/dfa/DFA.java
@@ -38,8 +38,10 @@ import org.antlr.v4.runtime.misc.NotNull;
 import org.antlr.v4.runtime.misc.Nullable;
 
 import java.util.ArrayList;
+import java.util.Collections;
+import java.util.Comparator;
+import java.util.HashMap;
 import java.util.HashSet;
-import java.util.LinkedHashMap;
 import java.util.List;
 import java.util.Map;
 import java.util.Set;
@@ -49,7 +51,7 @@ public class DFA {
 	 *  ({@link Set} only allows you to see if it's there).
      */
     @NotNull
-	public final Map<DFAState, DFAState> states = new LinkedHashMap<DFAState, DFAState>();
+	public final Map<DFAState, DFAState> states = new HashMap<DFAState, DFAState>();
 	@Nullable
 	public DFAState s0;
 
@@ -73,6 +75,22 @@ public class DFA {
 		this.decision = decision;
 	}
 
+	/**
+	 * Return a list of all states in this DFA, ordered by state number.
+	 */
+	@NotNull
+	public List<DFAState> getStates() {
+		List<DFAState> result = new ArrayList<DFAState>(states.keySet());
+		Collections.sort(result, new Comparator<DFAState>() {
+			@Override
+			public int compare(DFAState o1, DFAState o2) {
+				return o1.stateNumber - o2.stateNumber;
+			}
+		});
+
+		return result;
+	}
+
 	public List<Set<ATNState>> getATNStatesAlongPath(ParserATNSimulator atn,
 													 List<DFAState> dfaStates,
 													 TokenStream input, int start, int stop)
diff --git a/runtime/Java/src/org/antlr/v4/runtime/dfa/DFASerializer.java b/runtime/Java/src/org/antlr/v4/runtime/dfa/DFASerializer.java
index 81ab62d6a..4c2fe7c5b 100644
--- a/runtime/Java/src/org/antlr/v4/runtime/dfa/DFASerializer.java
+++ b/runtime/Java/src/org/antlr/v4/runtime/dfa/DFASerializer.java
@@ -34,7 +34,7 @@ import org.antlr.v4.runtime.misc.NotNull;
 import org.antlr.v4.runtime.misc.Nullable;
 
 import java.util.Arrays;
-import java.util.Map;
+import java.util.List;
 
 /** A DFA walker that knows how to dump them to serialized strings. */
 public class DFASerializer {
@@ -52,21 +52,20 @@ public class DFASerializer {
 	public String toString() {
 		if ( dfa.s0==null ) return null;
 		StringBuilder buf = new StringBuilder();
-		Map<DFAState,DFAState> states = dfa.states;
-		if ( states!=null ) {
-			for (DFAState s : states.values()) {
-				int n = 0;
-				if ( s.edges!=null ) n = s.edges.length;
-				for (int i=0; i<n; i++) {
-					DFAState t = s.edges[i];
-					if ( t!=null && t.stateNumber != Integer.MAX_VALUE ) {
-						buf.append(getStateString(s));
-						String label = getEdgeLabel(i);
-						buf.append("-").append(label).append("->").append(getStateString(t)).append('\n');
-					}
+		List<DFAState> states = dfa.getStates();
+		for (DFAState s : states) {
+			int n = 0;
+			if ( s.edges!=null ) n = s.edges.length;
+			for (int i=0; i<n; i++) {
+				DFAState t = s.edges[i];
+				if ( t!=null && t.stateNumber != Integer.MAX_VALUE ) {
+					buf.append(getStateString(s));
+					String label = getEdgeLabel(i);
+					buf.append("-").append(label).append("->").append(getStateString(t)).append('\n');
 				}
 			}
 		}
+
 		String output = buf.toString();
 		//return Utils.sortLinesInString(output);
 		return output;