Relax Operations.isTotal() to work with a deterministic automaton (#13707)

Improve Operations.isTotal() to work with non-minimal automata.

lucene/CHANGES.txt

@@ -169,6 +169,8 @@ Improvements
 
 * GITHUB#12172: Update Romanian stopwords list to include the modern unicode forms.  (Trey Jones)
 
+* GITHUB#13707: Improve Operations.isTotal() to work with non-minimal automata. (Dawid Weiss, Robert Muir)
+
 Optimizations
 ---------------------
 

lucene/core/src/java/org/apache/lucene/util/automaton/Operations.java

@@ -778,22 +778,48 @@ public final class Operations {
     return true;
   }
 
-  /** Returns true if the given automaton accepts all strings. The automaton must be minimized. */
+  /**
+   * Returns true if the given automaton accepts all strings.
+   *
+   * <p>The automaton must be deterministic, or this method may return false.
+   *
+   * <p>Complexity: linear in number of states and transitions.
+   */
   public static boolean isTotal(Automaton a) {
     return isTotal(a, Character.MIN_CODE_POINT, Character.MAX_CODE_POINT);
   }
 
   /**
    * Returns true if the given automaton accepts all strings for the specified min/max range of the
-   * alphabet. The automaton must be minimized.
+   * alphabet.
+   *
+   * <p>The automaton must be deterministic, or this method may return false.
+   *
+   * <p>Complexity: linear in number of states and transitions.
    */
   public static boolean isTotal(Automaton a, int minAlphabet, int maxAlphabet) {
-    if (a.isAccept(0) && a.getNumTransitions(0) == 1) {
-      Transition t = new Transition();
-      a.getTransition(0, 0, t);
-      return t.dest == 0 && t.min == minAlphabet && t.max == maxAlphabet;
+    BitSet states = getLiveStates(a);
+    Transition spare = new Transition();
+    int seenStates = 0;
+    for (int state = states.nextSetBit(0); state >= 0; state = states.nextSetBit(state + 1)) {
+      // all reachable states must be accept states
+      if (a.isAccept(state) == false) return false;
+      // all reachable states must contain transitions covering minAlphabet-maxAlphabet
+      int previousLabel = minAlphabet - 1;
+      for (int transition = 0; transition < a.getNumTransitions(state); transition++) {
+        a.getTransition(state, transition, spare);
+        // no gaps are allowed
+        if (spare.min > previousLabel + 1) return false;
+        previousLabel = spare.max;
+      }
+      if (previousLabel < maxAlphabet) return false;
+      if (state == Integer.MAX_VALUE) {
+        break; // or (state+1) would overflow
+      }
+      seenStates++;
     }
-    return false;
+    // we've checked all the states, automaton is either total or empty
+    return seenStates > 0;
   }
 
   /**

lucene/core/src/test/org/apache/lucene/util/automaton/TestOperations.java

@@ -173,6 +173,42 @@ public class TestOperations extends LuceneTestCase {
     assertTrue(exc.getMessage().contains("input automaton is too large"));
   }
 
+  public void testIsTotal() {
+    // minimal
+    assertFalse(Operations.isTotal(Automata.makeEmpty()));
+    assertFalse(Operations.isTotal(Automata.makeEmptyString()));
+    assertTrue(Operations.isTotal(Automata.makeAnyString()));
+    assertTrue(Operations.isTotal(Automata.makeAnyBinary(), 0, 255));
+    assertFalse(Operations.isTotal(Automata.makeNonEmptyBinary(), 0, 255));
+    // deterministic, but not minimal
+    assertTrue(Operations.isTotal(Operations.repeat(Automata.makeAnyChar())));
+    Automaton tricky =
+        Operations.repeat(
+            Operations.union(
+                Automata.makeCharRange(Character.MIN_CODE_POINT, 100),
+                Automata.makeCharRange(101, Character.MAX_CODE_POINT)));
+    assertTrue(Operations.isTotal(tricky));
+    // not total, but close
+    Automaton tricky2 =
+        Operations.repeat(
+            Operations.union(
+                Automata.makeCharRange(Character.MIN_CODE_POINT + 1, 100),
+                Automata.makeCharRange(101, Character.MAX_CODE_POINT)));
+    assertFalse(Operations.isTotal(tricky2));
+    Automaton tricky3 =
+        Operations.repeat(
+            Operations.union(
+                Automata.makeCharRange(Character.MIN_CODE_POINT, 99),
+                Automata.makeCharRange(101, Character.MAX_CODE_POINT)));
+    assertFalse(Operations.isTotal(tricky3));
+    Automaton tricky4 =
+        Operations.repeat(
+            Operations.union(
+                Automata.makeCharRange(Character.MIN_CODE_POINT, 100),
+                Automata.makeCharRange(101, Character.MAX_CODE_POINT - 1)));
+    assertFalse(Operations.isTotal(tricky4));
+  }
+
   /**
    * Returns the set of all accepted strings.
    *