remove_fin: remove useless states

* src/tgba/tgbagraph.cc (purge_dead_states): Using a DFS to compute a
topological order, allowing to remove useless using a second
pass (instead of iterating the passes until there is nothing to remove).
* src/tgbaalgos/remfin.cc: Call purge_dead_states().
* src/tgbatest/remfin.test, src/tgbatest/det.test: Adjust expected
output.
* doc/org/autfilt.org: Update example.

doc/org/autfilt.org

@@ -335,11 +335,11 @@ $txt
 #+RESULTS:
 [[file:autfilt-ex1.png]]
 
-Using =--sba= will "push" the acceptance membership of the transitions to the states:
+Using =--sbacc= will "push" the acceptance membership of the transitions to the states:
 
 #+NAME: autfilt-ex2
 #+BEGIN_SRC sh :results verbatim :export code
-autfilt --sba aut-ex1.hoa --dot=.a
+autfilt --sbacc aut-ex1.hoa --dot=.a
 #+END_SRC
 
 #+RESULTS: autfilt-ex2
@@ -430,15 +430,9 @@ digraph G {
   2 -> 0 [label=<!b>]
   2 -> 1 [label=<a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
   2 -> 2 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
-  2 -> 3 [label=<!b>]
+  2 -> 3 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
-  2 -> 4 [label=<a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
-  2 -> 5 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
   3 [label="3"]
-  4 [label="4"]
+  3 -> 3 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font><font color="#60BD68">❹</font>>]
-  5 [label="5"]
-  5 -> 3 [label=<!b<br/><font color="#F17CB0">❶</font><font color="#60BD68">❹</font>>]
-  5 -> 4 [label=<a &amp; !b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font><font color="#60BD68">❹</font>>]
-  5 -> 5 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font><font color="#60BD68">❹</font>>]
 }
 #+end_example
 

src/tgba/tgbagraph.cc

@@ -178,52 +178,74 @@ namespace spot
     unsigned num_states = g_.num_states();
     if (num_states == 0)
       return;
-    std::vector<unsigned> info(num_states, 0);
+
-    // In this loop, info[s] means that the state is useless.
+    std::vector<unsigned> useful(num_states, 0);
-    bool untouched;
+
+    // Make a DFS to compute a topological order.
+    std::vector<unsigned> order;
+    order.reserve(num_states);
+    std::vector<std::pair<unsigned, unsigned>> todo; // state, trans
+    useful[init_number_] = 1;
+    todo.emplace_back(init_number_, g_.state_storage(init_number_).succ);
     do
       {
-	untouched = true;
+	unsigned src;
-	for (unsigned s = 0; s < num_states; ++s)
+	unsigned tid;
+	std::tie(src, tid) = todo.back();
+	if (tid == 0U)
 	  {
-	    if (info[s])
+	    todo.pop_back();
-	      continue;
+	    order.push_back(src);
-	    bool useless = true;
+	    continue;
-	    auto t = g_.out_iteraser(s);
+	  }
-	    while (t)
+	auto& t = g_.trans_storage(tid);
-	      {
+	todo.back().second = t.next_succ;
-		// Erase any transition to a unused state.
+	unsigned dst = t.dst;
-		if (info[t->dst])
+	if (useful[dst] != 1)
-		  {
+	  {
-		    t.erase();
+	    todo.emplace_back(dst, g_.state_storage(dst).succ);
-		    continue;
+	    useful[dst] = 1;
-		  }
-		// if we have a transition, to a used state,
-		// then the state is useful.
-		useless = false;
-		++t;
-	      }
-	    if (useless)
-	      {
-		info[s] = true;
-		untouched = false;
-	      }
 	  }
       }
-    while (!untouched);
+    while (!todo.empty());
+
+    // Process states in topological order
+    for (auto s: order)
+      {
+	auto t = g_.out_iteraser(s);
+	bool useless = true;
+	while (t)
+	  {
+	    // Erase any transition to a useless state.
+	    if (!useful[t->dst])
+	      {
+		t.erase();
+		continue;
+	      }
+	    // if we have a transition to a useful state, then the
+	    // state is useful.
+	    useless = false;
+	    ++t;
+	  }
+	if (useless)
+	  useful[s] = 0;
+      }
+
+    // Make sure the initial state is useful (even if it has been
+    // marked as useless by the previous loop because it has no
+    // successor).
+    useful[init_number_] = 1;
 
-    // Assume that the initial state is useful.
-    info[init_number_] = false;
     // Now renumber each used state.
     unsigned current = 0;
-    for (auto& v: info)
+    for (unsigned s = 0; s < num_states; ++s)
-      if (v)
+      if (useful[s])
-	v = -1U;
+	useful[s] = current++;
       else
-	v = current++;
+	useful[s] = -1U;
-    if (current == info.size())
+    if (current == num_states)
       return;			// No useless state.
-    init_number_ = info[init_number_];
+    init_number_ = useful[init_number_];
-    g_.defrag_states(std::move(info), current);
+    g_.defrag_states(std::move(useful), current);
   }
 }

src/tgbaalgos/remfin.cc

@@ -331,7 +331,7 @@ namespace spot
 
 
       }
-    res->purge_unreachable_states();
+    res->purge_dead_states();
     trace << "before cleanup: " << res->get_acceptance() << '\n';
     cleanup_acceptance(res);
     trace << "after cleanup: " << res->get_acceptance() << '\n';

src/tgbatest/det.test

@@ -80,15 +80,14 @@ State: 2
 --END--
 EOF
 
-# FIXME: we should improve this output
 cat >ex.hoa <<'EOF'
 HOA: v1
-States: 7
+States: 5
 Start: 0
 AP: 1 "a"
 acc-name: Buchi
 Acceptance: 1 Inf(0)
-properties: trans-labels explicit-labels state-acc
+properties: trans-labels explicit-labels state-acc inherently-weak
 --BODY--
 State: 0
 [!0] 0
@@ -102,16 +101,12 @@ State: 2
 [!0] 0
 [0] 2
 [!0] 3
-[0] 5
+[0] 4
 State: 3 {0}
 [!0] 3
 State: 4 {0}
 [!0] 3
-State: 5 {0}
+[0] 4
-[!0] 3
-[0] 5
-State: 6 {0}
-[t] 6
 --END--
 EOF
 
@@ -119,8 +114,6 @@ run 0 ../ltl2tgba -H -DC -XH in.hoa > out.hoa
 run 1 ../../bin/autfilt -q --are-isomorph in.hoa out.hoa
 run 0 ../../bin/autfilt -q --are-isomorph ex.hoa out.hoa
 
-# FIXME: State 2 and 5 are unreachable and I'd rather
-# not show them.
 run 0 ../ltl2tgba -x -DC 'GFa & XGFb' > out.tgba
 cat >ex.tgba <<EOF
 digraph G {
@@ -131,16 +124,12 @@ digraph G {
   0 -> 1 [label="1"]
   1 [label="1"]
   1 -> 1 [label="1"]
-  1 -> 3 [label="!a"]
+  1 -> 2 [label="!a"]
-  1 -> 4 [label="!b"]
+  1 -> 3 [label="!b"]
   2 [label="2", peripheries=2]
-  2 -> 3 [label="!a"]
+  2 -> 2 [label="!a"]
   3 [label="3", peripheries=2]
-  3 -> 3 [label="!a"]
+  3 -> 3 [label="!b"]
-  4 [label="4", peripheries=2]
-  4 -> 4 [label="!b"]
-  5 [label="5", peripheries=2]
-  5 -> 5 [label="1"]
 }
 EOF
 diff out.tgba ex.tgba

src/tgbatest/remfin.test

@@ -186,7 +186,7 @@ State: 2 {0}
 [0&!1] 2
 --END--
 HOA: v1
-States: 6
+States: 4
 Start: 0
 AP: 2 "a" "b"
 Acceptance: 4 Inf(0) | Inf(3) | (Inf(1)&Inf(2))
@@ -204,18 +204,12 @@ State: 2
 [!1] 0
 [0&!1] 1
 [!0&!1] 2
-[!1] 3
+[!0&!1] 3
-[0&!1] 4
-[!0&!1] 5
 State: 3
-State: 4
+[!0&!1] 3 {0}
-State: 5
-[!1] 3
-[0&!1] 4 {0}
-[!0&!1] 5 {0}
 --END--
 HOA: v1
-States: 6
+States: 4
 Start: 0
 AP: 2 "a" "b"
 Acceptance: 5 (Inf(0)&Inf(1)&Inf(4)) | Inf(0) | (Inf(2)&Inf(3))
@@ -233,15 +227,9 @@ State: 2
 [!1] 0
 [0&!1] 1 {0}
 [!0&!1] 2 {0}
-[!1] 3
+[!0&!1] 3 {0}
-[0&!1] 4 {0}
-[!0&!1] 5 {0}
 State: 3
-State: 4
+[!0&!1] 3 {0 1 4}
-State: 5
-[!1] 3 {1 4}
-[0&!1] 4 {0 1 4}
-[!0&!1] 5 {0 1 4}
 --END--
 HOA: v1
 States: 1
@@ -281,7 +269,7 @@ State: 1 {0}
 [0] 1
 --END--
 HOA: v1
-States: 12
+States: 10
 Start: 2
 AP: 1 "p1"
 Acceptance: 2 Inf(1) | Inf(0)
@@ -290,8 +278,8 @@ properties: trans-labels explicit-labels state-acc
 State: 0
 [!0] 6
 [0] 0
+[0] 8
 [0] 9
-[0] 11
 State: 1 {0 1}
 [!0] 3
 [0] 3
@@ -314,13 +302,9 @@ State: 7 {1}
 [!0] 6
 [0] 4
 State: 8
-State: 9
+[0] 8
-[!0] 8
+State: 9 {1}
 [0] 9
-State: 10
-State: 11 {1}
-[!0] 10
-[0] 11
 --END--
 EOF